CComplex Class

CComplex is a class to work with complex numbers with Free Basic. Complex numbers are represented using the type _complex. The real and imaginary part are stored in the members x and y. There is also a flat api version that you can use alone or in combination with this class (see: Complex Numbers Procedures

TYPE _complex
   x AS DOUBLE   ' real part
   y AS DOUBLE   ' imaginary part
END TYPE

Include file: CComplex.inc.

Constructors

Create a new instance of the CComplex class and assigns the values passed to it.

CONSTRUCTOR CComplex
CONSTRUCTOR CComplex (BYVAL x AS DOUBLE = 0, BYVAL y AS DOUBLE = 0)
CONSTRUCTOR CComplex (BYREF cpx AS CComplex)
CONSTRUCTOR CComplex (BYREF cpx AS _complex)

Examples

Uses the cartesian components (x,y) to set the real and imaginary parts of the complex number.

DIM cpx AS CComplex = TYPE(3, 4)
DIM cpx2 AS CComplex = cpx

An instance of the CComplex class.

DIM cpx AS CComplex = TYPE(3, 4)
DIM cpx2 AS CComplex = cpx

A _complex structure.

DIM cpx AS CComplex = TYPE<_complex>(3, 4)

Operators

Methods and Properties

Helper Methods

Operator LET (=)

Assigns a value to a CComplex variable.

OPERATOR LET (BYREF z AS CComplex)
OPERATOR LET (BYREF z AS _complex)

An instance of the CComplex class.

DIM cpx AS CComplex = TYPE(3, 4)
DIM cpx2 AS CComplex = cpx

DIM cpx AS CComplex
cpx = CComplex(3, 4)

A _complex structure.

DIM cpx AS CComplex = TYPE<_complex>(3, 4)

Operator CAST

Returns the underlying _complex number.

OPERATOR CAST () AS _complex
OPERATOR CAST () AS STRING

Remarks

This overloaded operator is not called directly.

The second overloaded operator returns the complex number as a formatted string that can be used with the PRINT statement.

Comparison operators

Compares complex numbers for equality or inequality.

OPERATOR = (BYREF z1 AS CComplex, BYREF z2 AS CComplex) AS BOOLEAN
OPERATOR <> (BYREF z1 AS CComplex, BYREF z2 AS CComplex) AS BOOLEAN

Exammple

DIM cpx1 AS CComplex = CComplex(1, 2)
DIM cpx2 AS CComplex = CComplex(3, 4)
IF cpx1 = cpx2 THEN PRINT "equal" ELSE PRINT "different"

Math operators

OPERATOR + (BYREF z1 AS CComplex, BYREF z2 AS CComplex) AS CComplex
OPERATOR + (BYVAL a AS DOUBLE, BYREF z AS CComplex) AS CComplex
OPERATOR + (BYREF z AS CComplex, BYVAL a AS DOUBLE) AS CComplex
OPERATOR - (BYREF z1 AS CComplex, BYREF z2 AS CComplex) AS CComplex
OPERATOR - (BYVAL a AS DOUBLE, BYREF z AS CComplex) AS CComplex
OPERATOR - (BYREF z AS CComplex, BYVAL a AS DOUBLE) AS CComplex
OPERATOR * (BYREF z1 AS CComplex, BYREF z2 AS CComplex) AS CComplex
OPERATOR * (BYVAL a AS DOUBLE, BYREF z AS CComplex) AS CComplex
OPERATOR * (BYREF z AS CComplex, BYVAL a AS DOUBLE) AS CComplex
OPERATOR / (BYREF leftside AS CComplex, BYREF rightside AS CComplex) AS CComplex
OPERATOR / (BYVAL a AS DOUBLE, BYREF z AS CComplex) AS CComplex
OPERATOR / (BYREF z AS CComplex, BYVAL a AS DOUBLE) AS CComplex
OPERATOR += (BYREF z AS CComplex)
OPERATOR -= (BYREF z AS CComplex)
OPERATOR *= (BYREF z AS CComplex)
OPERATOR /= (BYREF z AS CComplex)
OPERATOR - (BYREF z AS CComplex, BYVAL a AS DOUBLE) AS CComplex
OPERATOR ^ (BYREF value AS CComplex, BYREF power AS CComplex) AS CComplex
OPERATOR ^ (BYREF value AS CComplex, BYVAL power AS DOUBLE) AS CComplex

Examples

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex(5, 6)
cpx2 = cpx1 + cpx2

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex = CComplex(5, 6)
cpx2 = cpx1 + 11

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex = CComplex(5, 6)
cpx2 = 11 + cpx1

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex = CComplex(5, 6)
cpx2 = cpx1 - cpx2

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex
cpx2 = cpx1 - 11

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex
cpx2 = 11 - cpx1

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex = CComplex(5, 6)
cpx2 = cpx1 * cpx2

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex
cpx2 = cpx1 * 11

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex
cpx2 = 11 * cpx1

DIM cpx1 AS CComplex = CComplex(5, 6)
DIM cpx2 AS CComplex = CComplex(2, 3)
cpx2 = cpx1 / cpx2

DIM cpx1 AS CComplex = CComplex(5, 6)
DIM cpx2 AS CComplex
cpx2 = cpx1 / 11

DIM cpx1 AS CComplex = CComplex(5, 6)
DIM cpx2 AS CComplex
cpx2 = 11 / cpx1

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex = CComplex(5, 6)
cpx1 += cpx2

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex = CComplex(5, 6)
cpx2 -= cpx1

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex = CComplex(5, 6)
cpx1 *= cpx2

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex = CComplex(5, 6)
cpx2 /= cpx1

DIM cpx1 AS CComplex = CComplex(3, 4)
DIM cpx2 AS CComplex = -cpx1

CAbs / CMagnitude

Returns the magnitude of this complex number.

FUNCTION CAbs () AS DOUBLE
FUNCTION CMagnitude () AS DOUBLE

Example

DIM cpx AS CComplex = CComplex(2, 3)
PRINT cpx.CAbs
Output: 3.60555127546399

CAbs2 / CNorm

Returns the squared magnitude of this complex number, otherwise known as the complex norm.

FUNCTION CAbs2 () AS DOUBLE
FUNCTION CNorm () AS DOUBLE

Example

DIM cpx AS CComplex = CComplex(2, 3)
PRINT cpx.CAbs2
Output: 13

CAbsSqr

Returns the absolute square (squared norm) of a complex number.

FUNCTION CAbsSqr () AS DOUBLE

Example

DIM cpx AS CComplex = CComplex(1.2345, -2.3456)
print cpx.CAbsSqr
Output: 7.025829610000001

CAdd

Adds a complex number.

FUNCTION CAdd (BYREF z AS CComplex) AS CComplex
FUNCTION CAdd (BYVAL x AS DOUBLE, BYVAL y AS DOUBLE) AS CComplex

Examples

DIM cpx AS CComplex = CComplex(5, 6)
DIM cpx2 AS CComplex = CComplex(2, 3)
cpx = cpx.CAdd(cpx2)
' --or-- cpx = cpx.CAdd(CComplex(2, 3))

DIM cpx AS CComplex = CComplex(5, 6) : cpx = cpx.CAdd(2, 3)

CAddImag

Adds an imaginary number.

FUNCTION CAddImag (BYVAL x AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex = CComplex(5, 6)
cpx = cpx.CAddImag(10)

CAddReal

Adds a real number.

FUNCTION CAddReal (BYVAL x AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex = CComplex(5, 6)
cpx = cpx.CAddReal(10)

CArcCos / CACos

Returns the complex arccosine of this complex number.

FUNCTION CArcCos () AS CComplex
FUNCTION CACos () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
print cpx.CArcCos(z)
Output: 0.9045568943023814 -1.061275061905036 * i

CArcCosH / CACosH

Returns the complex hyperbolic arccosine of this complex number. The branch cut is on the real axis, less than 1.

FUNCTION CArcCosH () AS CComplex
FUNCTION CACosH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
print cpx.CArcCosH
Output: 1.061275061905036 +0.9045568943023813 * i

CArcCosHReal / CACosHReal

Returns the complex hyperbolic arccosine of a real number.

FUNCTION CArcCosHReal (BYVAL value AS DOUBLE) AS CComplex
FUNCTION CACosHReal (BYVAL value AS DOUBLE) AS CComplex

CArcCosReal / CACosReal

Returns the complex arccosine of a real number.
For a between -1 and 1, the function returns a real value in the range [0, pi].
For a less than -1 the result has a real part of pi and a negative imaginary part.
For a greater than 1 the result is purely imaginary and positive.

FUNCTION CArcCosReal (BYVAL value AS DOUBLE) AS CComplex
FUNCTION CACosReal (BYVAL value AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex
print cpx.CArcCosReal(1) ' = 0 0 * i
print cpx.CArcCosReal(-1) ' = 3.141592653589793 0 * i
print cpx.CArcCosReal(2) ' = 0 +1.316957896924817 * i

CArcCot / CACot

Returns the complex arccotangent of this complex number.

FUNCTION CArcCot () AS CComplex
FUNCTION CACot () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
print cpx.CArcCot
Output: 0.5535743588970452 -0.4023594781085251 * i

CArcCotH / CACotH

Returns the complex hyperbolic arccotangent of this complex number.

FUNCTION CArcCotH () AS CComplex
FUNCTION CACotH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CArcCotH
Output: 0.4023594781085251 -0.5535743588970452 * i

CArcCsc / CACsc

Returns the complex arccosecant of this complex number.

FUNCTION CArcCsc () AS CComplex
FUNCTION CACsc () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
print cpx.CArcCsc
Output: 0.4522784471511907 -0.5306375309525178 * i

CArcCscH / CACscH

Returns the complex hyperbolic arccosecant of this complex number.

FUNCTION CArcCscH () AS CComplex
FUNCTION CACscH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CArcCscH
Output: 0.5306375309525179 -0.4522784471511906 * i

CArcCscReal / CACscReal

Returns the complex arccosecant of a real number.

FUNCTION CArcCscReal (BYVAL value AS DOUBLE) AS CComplex
FUNCTION CACscReal (BYVAL value AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex
print cpx.CArcCscReal(1)
Output: 1.570796326794897 0 * i

CArcSec / CASec

Returns the complex arcsecant of this complex number.

FUNCTION CArcSec () AS CComplex
FUNCTION CASec () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
print cpx.CArcSec
Output: 1.118517879643706 +0.5306375309525176 * i

CArcSecH / CASecH

Returns the complex hyperbolic arcsecant of this complex number.

FUNCTION CArcSecH () AS CComplex
FUNCTION CASecH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CArcSecH
Output: 0.5306375309525178 -1.118517879643706 * i

CArcSecReal / CASecReal

Returns the complex arcsecant of a real number.

FUNCTION CArcSecReal (BYVAL value AS DOUBLE) AS CComplex
FUNCTION CASecReal (BYVAL value AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex
print cpx.CArcSecReal(1.1)
Output: 0.4296996661514246 0 * i

CArcSin / CASin

Returns the complex arcsine of this complex number. The branch cuts are on the real axis, less than -1 and greater than 1.

FUNCTION CArcSin () AS CComplex
FUNCTION CASin () AS CComplex

Example

DIM cpx AS CComplex
PRINT cpx.CArcSin(1, 1)
Output: 0.6662394324925152 +1.061275061905036 * i

CArcSinH / CASinH

Returns the complex hyperbolic arcsine of this complex number. The branch cuts are on the imaginary axis, below -i and above i.

FUNCTION CArcSinH () AS CComplex
FUNCTION CASinH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CArcSinH
Output: 1.061275061905036 +0.6662394324925153 * i

CArcSinReal / CASinReal

Returns the complex arcsine of a real number.
For a between -1 and 1, the function returns a real value in the range [-pi/2, pi/2].
For a less than -1 the result has a real part of -pi/2 and a positive imaginary part.
For a greater than 1 the result has a real part of pi/2 and a negative imaginary part.

FUNCTION CArcSinReal (BYVAL value AS DOUBLE) AS CComplex
FUNCTION CASinReal (BYVAL value AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex
PRINT cpx.CArcSinReal(1)
Output: 1.570796326794897 +0 * i

CArcTan / CATan

Returns the complex arctangent of this complex number. The branch cuts are on the imaginary axis, below -i and above i.

FUNCTION CArcTan () AS CComplex
FUNCTION CATan () AS CComplex

Example

DIM cpx AS CComplex
PRINT cpx.CArcTan(1, 1)
Output: 1.017221967897851 +0.4023594781085251 * i

CArcTanH / CATanH

Returns the complex hyperbolic arctangent of this complex number. The branch cuts are on the real axis, less than -1 and greater than 1.

FUNCTION CArcTanH () AS CComplex
FUNCTION CATanH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CArcTanH
Output: 0.4023594781085251 +1.017221967897851 * i

CArcTanHReal / CATanHReal

Returns the complex hyperbolic arctangent of a real number.

FUNCTION CArcTanHReal (BYVAL value AS DOUBLE) AS CComplex
FUNCTION CATanHReal (BYVAL value AS DOUBLE) AS CComplex

CArg / CArgument / CPhase

Returns the argument of this complex number.

FUNCTION CArg () AS DOUBLE
FUNCTION CArgument () AS DOUBLE
FUNCTION CPhase () AS DOUBLE

Example

DIM cpx AS CComplex = CComplex(1, 0)
PRINT cpx.CArg
Output: 0.0

DIM cpx AS CComplex = CComplex(0, 1)
PRINT cpx.CArg
Output: 1.570796326794897

DIM cpx AS CComplex = CComplex(0, -1)
PRINT cpx.CArg
Output: -1.570796326794897

DIM cpx AS CComplex = CComplex(-1, 0)
PRINT cpx.CArg
Output: 3.141592653589793

CConjugate / CConj

Returns the complex conjugate of this complex number.

FUNCTION CConjugate () AS CComplex
FUNCTION CConj () AS CComplex

Example

DIM cpx AS CComplex = CComplex(5, 6)
cpx = cpx.CConjugate

CCos

Returns the complex cosine of this complex number.

FUNCTION CCos () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CCos
Output: 0.8337300251311491 -0.9888977057628651 * i

CCosH

Returns the complex hyperbolic cosine of this complex number.

FUNCTION CCosH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CCosH
Output: 0.8337300251311491 +0.9888977057628651 * i

CCot

Returns the complex cotangent of this complex number.

FUNCTION CCot () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CCot
Output: 0.2176215618544027 -0.8680141428959249 * i

CCotH

Returns the complex hyperbolic cotangent of this complex number.

FUNCTION CCotH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CCotH
Output: 0.8680141428959249 -0.2176215618544029 * i

CCsc

Returns the complex cosecant of this complex number.

FUNCTION CCsc () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CCsc
Output: 0.6215180171704285 -0.3039310016284265 * i

CCscH

Returns the complex hyperbolic cosecant of this complex number.

FUNCTION CCscH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CCscH
Output: 0.3039310016284265 -0.6215180171704285 * i

CDiv

Divides by a complex number.
Divides by a real and an imaginary number.

FUNCTION CDiv (BYREF z AS CComplex) AS CComplex
FUNCTION CDiv (BYVAL x AS DOUBLE, BYVAL y AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex = CComplex(5, 6)
DIM cpx2 AS CComplex = CComplex(2, 3)
cpx = cpx.CDiv(cpx2)
' --or-- cpx = cpx.CDiv(CComplex(2, 3))

DIM cpx AS CComplex = CComplex(5, 6)
cpx = cpx.CDiv(2, 3)

CDivImag

Divides by an imaginary number.

FUNCTION CDivImag (BYVAL y AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex = CComplex(5, 6)
cpx = cpx.CDivImag(10)

CDivReal

Divides by a real number.

FUNCTION CDivReal (BYVAL x AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex = CComplex(5, 6)
cpx = cpx.CDivReal(10)

CExp

Returns the complex exponential of this complex number.

FUNCTION CExp () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CExp
Output: 1.468693939915885 +2.287355287178842 * i

CImag

Gets/sets the imaginary part of a complex number.

PROPERTY CImag () AS DOUBLE
PROPERTY CImag (BYVAL x AS DOUBLE)

Example

DIM cpx AS CComplex : cpx.CImag = 4
DIM d AS DOUBLE = cpx.CImag

CLog

Returns the complex natural logarithm (base e) of this complex number. The branch cut is the negative real axis.

FUNCTION CLog () AS CComplex
FUNcTION CLog (BYVAL baseValue AS DOUBLE) AS CComplex

Examples

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CLog
Output: 0.3465735902799727 +0.7853981633974483 * i

DIM cpx AS CComplex = CComplex(0, 0)
PRINT cpx.CLog
Output: -1.#INF

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CLog(10)
Output: 0.1505149978319906 +0.3410940884604603 * i

CLog10

Returns the complex base-10 logarithm of this complex number.

FUNCTION CLog10 () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CLog10
Output: 0.1505149978319906 +0.3410940884604603 * i

CLogAbs

Returns the natural logarithm of the magnitude of the complex number z, log|z|. It allows an accurate evaluation of \log|z| when |z| is close to one. The direct evaluation of log(CAbs(z)) would lead to a loss of precision in this case.

FUNCTION CLogAbs () AS DOUBLE

Example

DIM cpx AS CComplex = CComplex(1.1, 0.1)
PRINT cpx.CLogAbs
Output: 0.09942542937258279

CModulus / CMod

Returns the modulus of a complex number.

FUNCTION CModulus () AS DOUBLE
FUNCTION CMod () AS DOUBLE

Example

DIM cpx AS CComplex = CComplex(2.3, -4.5)
print cpx.CModulus
Output: 5.053711507397311

CMul

Multiplies by a complex number.
Multiplies by a real and an imaginary number.

FUNCTION CMul (BYREF z AS CComplex) AS CComplex
FUNCTION CMul (BYVAL x AS DOUBLE, BYVAL y AS DOUBLE) AS CComplex

Examples

DIM cpx AS CComplex = CComplex(5, 6)
DIM cpx2 AS CComplex = CComplex(2, 3)
cpx = cpx.CMul(cpx2)
' --or-- cpx = cpx.CMul(CComplex(2, 3))

DIM cpx AS CComplex = CComplex(5, 6)
cpx = cpx.CMul(2, 3)

CMulImag

Multiplies by an imaginary number.

FUNCTION CMulImag (BYVAL y AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex = CComplex(5, 6)
cx = cpx.CMulImag(3)

CMulReal

Multiplies by a real number.

FUNCTION CMulReal (BYVAL x AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex = CComplex(5, 6)
cpx = cpx.CMulReal(2)

CNegate / CNeg / CNegative

Negates the complex number.

FUNCTION CNeg (BYREF z AS _complex) AS _complex
FUNCTION CNegate (BYREF z AS _complex) AS _complex
FUNCTION CNegative (BYREF z AS _complex) AS _complex

CNthRoot

Returns the kth nth root of a complex number where k = 0, 1, 2, 3,...,n - 1.
De Moivre's formula states that for any complex number x and integer n it holds that
cos(x)+ isin(x))^n = cos(nx) + isin(nx)
where i is the imaginary unit (i2 = -1).
Since z = re^(it) = r * (cos(t) + i sin(t))
where
z = (a, ib)
r = modulus of z
t = argument of z
i = sqrt(-1.0)
we can calculate the nth root of z by the formula:
z^(1/n) = r^(1/n) * (cos(x/n) + i sin(x/n))
by using log division.

FUNCTION CNthRoot (BYVAL n AS LONG, BYVAL k AS LONG = 0) AS _complex

Example

DIM cpx AS CComplex = CComplex(2.3, -4.5)
DIM n AS LONG = 5
FOR i AS LONG = 0 TO n - 1
   print CStr(cpx.CNthRoot(n, i))
NEXT
Output:
 1.349457704883236  -0.3012830564679053 * i
 0.7035425781022545 +1.190308959128094 * i
-0.9146444790833151 +1.036934450322577 * i
-1.268823953798186  -0.5494482247230521 * i
 0.1304681498960107 -1.376512128259714 * i

CPolar

Sets the complex number from the polar representation.

FUNCTION CPolar (BYVAL r AS DOUBLE, BYVAL theta AS DOUBLE)

CPow

Returns this complex number raised to a complex power.
Returns this complex number raised to a real number.

FUNCTION CPow (BYREF power AS CComplex) AS CComplex
FUNCTION CPow (BYVAL power AS DOUBLE) AS CComplex

Examples

DIM cpx AS CComplex = CComplex(1, 1)
DIM b AS CComplex = CComplex(2, 2)
PRINT cpx.CPow(b)
Output: -0.2656539988492412 +0.3198181138561362 * i

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CPow(2)
Output: 1.224606353822378e-016 +2 * i

CReal

Gets/sets the real part of a complex number.

PROPERTY CReal () AS DOUBLE
PROPERTY CReal (BYVAL x AS DOUBLE)

Example

DIM cpx AS CComplex : cpx.CReal = 3
DIM d AS DOUBLE = cpx.CReal

CReciprocal / CInverse

Returns the inverse, or reciprocal, of a complex number.

FUNCTION CReciprocal () AS CComplex
FUNCTION CInverse () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
Print cpx.CReciprocal
Output: 0.5 -0.5 * i

CSec

Returns the complex secant of this complex number.

FUNCTION CSec () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CSec
Output: 0.4983370305551869 +0.591083841721045 * i

CSecH

Returns the complex hyperbolic secant of this complex number.

FUNCTION CSecH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CSecH
Output: 0.4983370305551869 -0.591083841721045 * i

CSet / CRect

Uses the cartesian components (x,y) to set the real and imaginary parts of the complex number.

PROPERTY CSet (BYVAL x AS DOUBLE, BYVAL y AS DOUBLE)
PROPERTY CRect (BYVAL x AS DOUBLE, BYVAL y AS DOUBLE)

Example

DIM cpx AS CComplex : cpx.CSet = 3, 4
DIM cpx AS CComplex : cpx.CRect = 3, 4

CSgn

Returns the sign of this complex number.
If number is greater than zero, then CSgn returns 1.
If number is equal to zero, then CSgn returns 0.
If number is less than zero, then CSgn returns -1.

PROPERTY CSgn () AS LONG

CSin

Returns the complex sine of this complex number.

PROPERTY CSin () AS CSin

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CSin
Output: 1.298457581415977 +0.6349639147847361 * i

CSinH

Returns the complex hyperbolic sine of this complex number.

FUNCTION CSinH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CSinH
Output: 0.6349639147847361 +1.298457581415977 * i

CSqr / CSqrt

Returns the square root of the complex number z. The branch cut is the negative real axis. The result always lies in the right half of the complex plane.

FUNCTION CSqr () AS CComplex
FUNCTION CSqrt () AS CComplex

Returns the complex square root of the real number x, where x may be negative.

FUNCTION CSqr (BYVAL value AS DOUBLE) AS CComplex
FUNCTION CSqrt (BYVAL value AS DOUBLE) AS CComplex

Examples

DIM cpx AS CComplex = CComplex(2, 3)
PRINT cpx.CSqrt
Output: 1.67414922803554 +0.895977476129838 * i

Compute the square root of -1:

DIM cpx AS CComplex = CComplex(-1)
PRINT cpx.CSqr
Output: 0 +1.0 * i

CSub

Subtracts a complex number.

FUNCTION CSub (BYREF z AS CComplex) AS CComplex
FUNCTION CSub (BYVAL x AS DOUBLE, BYVAL y AS DOUBLE) AS CComplex

Examples

DIM cpx AS CComplex = CComplex(5, 6)
DIM cpx2 AS CComplex = CComplex(2, 3)
cpx = cpx.CSub(cpx2)
' --or-- cpx = cpx.CSub(CComplex(2, 3))

DIM cpx AS CComplex = CComplex(5, 6)
cpx = cpx.CSub(2, 3)

CSubImag

Subtracts an imaginary number.

FUNCTION CSubImag (BYVAL y AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex = CComplex(5, 6)
cx = cpx.CSubImag(3)

CSubReal

Subtracts a real number.

FUNCTION CSubReal (BYVAL x AS DOUBLE) AS CComplex

Example

DIM cpx AS CComplex = CComplex(5, 6)
cpx = cpx.CSubReal(2)

CSwap

Exchanges the contents of two complex numbers.

SUB CSwap (BYREF z AS CComplex)

CTan

Returns the complex tangent of this complex number.

FUNCTION CTan () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CTan
Output: 0.2717525853195117 +1.083923327338695 * i

CTanH

Returns the complex hyperbolic tangent of this complex number.

FUNCTION CTanH () AS CComplex

Example

DIM cpx AS CComplex = CComplex(1, 1)
PRINT cpx.CTanH
Output: 1.083923327338695 +0.2717525853195119 * i

ArcCosH

Calculates the inverse hyperbolic cosine.

FUNCTION ArcCosH (BYVAL x AS DOUBLE) AS DOUBLE

Example

DIM AS double pi = 3.1415926535
DIM AS double x, y
DIM cpx AS CComplex
x = cosh(pi / 4)
y = cpx.ArcCosH(x)
print "cosh = ", pi/4, x
print "ArcCosH = ", x, y

Output:
cosh =  0.785398163375      1.324609089232506
acosh = 1.324609089232506   0.7853981633749999

ArcTanH

Returns the inverse hyperbolic tangent of a number.

FUNCTION ArcTanH (BYVAL x AS DOUBLE) AS DOUBLE

Example

DIM cpx AS CComplex
print cpx.ArcTanh(0.76159416)
Output: 1.00000000962972

print cpx.ArcTanH(-0.1)
Output: -0.1003353477310756

IsInfinity / IsInf

Determines whether the argument is an infinity.

FUNCTION IsInfinity (BYVAL x AS DOUBLE) AS LONG
FUNCTION IsInf (BYVAL x AS DOUBLE) AS LONG

Remarks

Returns +1 if x is positive infinity, -1 if x is negative infinity and 0 otherwise.