f(z)    Complex Numbers and Functions     Tech Note

Verification Tests of ComplexMathLibrary Unit


The mathematics and usage of the ComplexMathLibrary unit is explained on the following pages:
Overview of complex numbers, in both rectangular and polar forms, and complex math with introductory explanation of software implementation and TComplex data type.
Complex arithmetic, including addition, subtraction, multiplication, and division.  Several other concepts are explained including complex conjugate, equality testing, and negation.
Logarithms and Powers
How to compute the complex natural logarithm and complex exponential.  A variety of related functions are also explained, including square, integer power, real power, complex power, and roots of complex values.
Trig Functions
How to compute several complex trigonometric functions, including cosine, sine, tangent, secant, cosecant, and cotangent.
Hyperbolic Functions
How to compute several complex hyperbolic functions, including hyperbolic cosine, hyperbolic sine, hyperbolic tangent, hyperbolic secant, hyperbolic cosecant, and hyperbolic cotangent.
Bessel Functions
How to compute the Bessel Functions J0 and I0.
Gamma Function
How to compute the gamma function for a complex argument, and also the natural logarithm of the complex gamma function.


Delphi 4/5/6 Source and EXE (232 KB):  ComplexMath.ZIP
- Includes Version.INC by Lasse Vågsæther Karlsen and is used with permission.  Updated for D6.
- Will not work in D3 since "default parameters" were used

Turbo Pascal unit:  Complex.ZIP
- Also online at 

Also see other Delphi Complex Math Resources

Updated 18 Feb 2002

since 23 June 2001