Complex Numbers

Complex numbers are ordered pairs of real numbers usually written as: x + iy (or x + yi), where x and y are real numbers. We may also denote a complex number by a single letter, for example ‘z’ such that z = x + yi.

The symbol ‘i’ is called the imaginary unit. The number x is called the real part of the complex number z and y is called the imaginary part of z.

There are many equations, for example x2 + 3 = 0, which can only be satisfied by complex numbers.

• Complex(realnumber, realnumber): Creates/returns a complex number

Example

(Basic)

DIM A
A = Complex(2.3, 4.5)

(Pascal)

var a;
a := Complex(2.3, 4.5);

RealPart(complexnumber): Returns the real part of a complex number

• ImaginaryPart(complexnumber): Returns the imaginary part of a complex number
• SetRealPart(complexnumber, realnumber): Changes the value of the real part of the complex number to the value specified by realnumber.
• SetImaginaryPart(complexnumber, realnumber): Changes the value of the imaginary part of the complex number to the value specified by realnumber.
• +, -, *, / operators: ArtSong’s implementation of complex numbers allows you to use the familiar addition, subtraction, multiplication, and division operators to represent basic mathematical operations on complex numbers

Complex Number Library Functions:

• VarIsComplex(variable): Returns a true or false value indicating whether ‘variable’ represents a complex number or not.
• RealPart(complexnumber): Returns the real part of a complex number.
• SetRealPart(complexnumber, realnumber): Changes the real part of a complex number.
• ImaginaryPart(complexnumber): Returns the imaginary part of a complex number.
• SetImaginaryPart(complexnumber, realnumber): Sets the imaginary part of a complex number.
• ComplexAbs(complexnumber): Returns the absolute value of a complex number.
• ComplexAbsSqr(complexnumber): Returns the square of the absolute value of a complex number
• ComplexAngle(complexnumber): Returns the angle made by a complex number.
• ComplexArcCos(complexnumber): Returns the inverse cosine of a complex number.
• ComplexArcCosH(complexnumber): Returns the hyperbolic inverse cosine of a complex number.
• ComplexArcCot(complexnumber): Returns the inverse cotangent of a complex number.
• ComplexArcCsc(complexnumber): Returns the hyperbolic inverse cotangent of a complex number.
• ComplexArcCscH(complexnumber): Returns the hyperbolic inverse cosecant of a complex number.
• ComplexArcSec(complexnumber): Returns the inverse secant of a complex number.
• ComplexArcSecH(complexnumber): Returns the hyperbolic inverse secant of a complex number.
• ComplexArcSin(complexnumber): Returns the inverse sine of a complex number.
• ComplexArcSinH(complexnumber): Returns the hyperbolic inverse sine of a complex number.
• ComplexArcTan(complexnumber): Returns the inverse tangent of a complex number.
• ComplexArcTanH(complexnumber): Returns the hyperbolic inverse tangent of a complex number.
• ComplexConjugate(complexnumber): Returns the conjugate of a complex number.
• ComplexCos(complexnumber): Returns the cosine of a complex number.
• ComplexCosH(complexnumber): Returns the hyperbolic cosine of a complex number.
• ComplexCot(complexnumber): Returns the cotangent of a complex number.
• ComplexCotH(complexnumber): Returns the hyperbolic cotangent of a complex number.
• ComplexCsc(complexnumber): Returns the cosecant of a complex number.
• ComplexCscH(complexnumber): Returns the hyperbolic cosecant of a complex number.
• ComplexExp(complexnumber): Returns the exponential of a complex number.
• ComplexFromPolar(complexnumber): Converts a set of polar coordinates to a complex number.
• ComplexInverse(complexnumber): Returns the inverse of a complex number.
• ComplexLn(complexnumber): Returns the natural log of a complex number.
• ComplexPower(complexnumber, complexpower): Returns the value of a complex number raised to a specified power.
• ComplexSec(complexnumber): Returns the secant of a complex number.
• ComplexSecH(complexnumber): Returns the hyperbolic secant of a complex number.
• ComplexSin(complexnumber): Returns the sine of a complex number.
• ComplexSinH(complexnumber): Returns the hyperbolic sine of a complex number.
• ComplexSqr(complexnumber): Returns the square of a complex number.
• ComplexSqrt(complexnumber): Returns the square root of a complex number.
• ComplexTan(complexnumber): Returns the tangent of a complex number.
• ComplexTanH(complexnumber): Returns the hyperbolic tangent of a complex number.
• ComplexTimesNegI(complexnumber): Returns the value of a complex number multiplied by –i.
• ComplexTimesPosI(complexnumber): Returns the value of a complex number multiplied by i.
• ComplexToPolar(complexnumber): Computes the polar coordinates that correspond to a custom Variant that represents a complex number.