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A C# class for complex numbers

, 3 Jul 2007 CPOL
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Implementation of the most common functions of complex numbers.

Introduction

Here you go: a simple but mathematically rigorous implementation of complex numbers in one small C# library. No problem in square rooting negative numbers anymore!

Functions

• Absolute value
• Addition
• Argument
• Conjugation
• Cosine
• Exponential function
• Exponentiation
• Division
• Hyperbolic functions (Sinh, Cosh, Tanh, Coth, Sech, Csch)
• Logarithm
• Multiplication
• Sine
• Square root
• Subtraction

Using the code

Either add a reference to CompLib.dll to your project, or directly use the class Complex.cs within your project.

The actual usage is intuitive:

```Complex I = Complex.I; // imaginary unit
Complex a = new Complex(1, 3); // inits a = 1+3i
Complex a2 = 1 + 3 * I; // a equals a2

Complex z = Complex.Pow((Complex.Sin(1/(1+I))), 1/3);```

Points of interest

One more thing: Complex logarithm is not a unique operation; the main value is computed as is common in the CAS world. E.g., the equation z^4 = -1 has four complex solutions, but only one is returned when trying "`z = Complex.Sqrt(Complex.Sqrt(-1));`" (as does Maple, for instance). This is due to the computation of the exponentiation:

`Pow(a,b) := Exp(b * Log(a))`

History

Coming soon

• init complex number with format string such as "3+4i" using regex.

Update July 3, 2007 #2

• Major bug in Arg() fixed (thanks Petr Stanislav!); this affects `Log()`, `Pow()`, and `Sqrt()`.

Update July 3, 2007

• Added hyperbolic functions.

Update June 10, 2007

• Replaced ^-operator with "`public static Complex Pow`", similar to `Math.Pow`.

Update June 7, 2007

• Added `Zero` and `One` as constants (e.g., use "`Complex z = Complex.One;`" instead of "`Complex z = new Complex(1)`").
• Major bug of division operation removed (using `a/b = a*Conj(b)*(1/(Abs(b)*Abs(b))` now).
• `ToString` method bug fixed.

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

About the Author

 Germany
No Biography provided

Comments and Discussions

 View All Threads First Prev Next
 Exponentiation ALWAYS binds more strongly than multiplication. sherifffruitfly3-Jun-07 11:08 sherifffruitfly 3-Jun-07 11:08
 Re: Exponentiation ALWAYS binds more strongly than multiplication. Keith Rule3-Jun-07 20:16 Keith Rule 3-Jun-07 20:16
 Re: Exponentiation ALWAYS binds more strongly than multiplication. peterchen3-Jun-07 22:20 peterchen 3-Jun-07 22:20
 Re: Exponentiation ALWAYS binds more strongly than multiplication. hanzzoid3-Jul-07 2:15 hanzzoid 3-Jul-07 2:15
 Re: Exponentiation ALWAYS binds more strongly than multiplication. PIEBALDconsult2-Apr-09 12:59 PIEBALDconsult 2-Apr-09 12:59
 Re: Exponentiation ALWAYS binds more strongly than multiplication. sherifffruitfly2-Apr-09 13:22 sherifffruitfly 2-Apr-09 13:22
 Re: Exponentiation ALWAYS binds more strongly than multiplication. PIEBALDconsult2-Apr-09 16:28 PIEBALDconsult 2-Apr-09 16:28
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