13,449,194 members (43,565 online)
alternative version

#### Stats

32K views
13 bookmarked
Posted 3 Jun 2007

# A C# class for complex numbers

, 3 Jul 2007
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
• 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 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.

## Share

 Germany
No Biography provided

## You may also be interested in...

 Pro

 First Prev Next
 code licence enrico.deg10-Jun-10 22:53 enrico.deg 10-Jun-10 22:53
 struct instead of class Member 190663510-Jun-08 1:17 Member 1906635 10-Jun-08 1:17
 Nice Lib but i would recommend changing "class Complex" to "struct Complex". Structs are more efficient for datatypes like this, especially where arrays (or lists) of Complex are needed. The current code will almost compile for "struct", just fix a few initialiser (Re to re, Im to im).
 Re: struct instead of class PIEBALDconsult2-Apr-09 12:56 PIEBALDconsult 2-Apr-09 12:56
 7-Zip will extract Dom Rositas20-Jun-07 16:22 Dom Rositas 20-Jun-07 16:22
 Re: 7-Zip will extract [modified] hanzzoid3-Jul-07 2:19 hanzzoid 3-Jul-07 2:19
 WinZip unknown compression type Dom Rositas20-Jun-07 7:49 Dom Rositas 20-Jun-07 7:49
 Cannot extract files from ZIP archive Tom14-Jun-07 3:54 Tom1 4-Jun-07 3:54
 Re: Cannot extract files from ZIP archive Tom118-Jun-07 5:39 Tom1 18-Jun-07 5:39
 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
 Last Visit: 31-Dec-99 18:00     Last Update: 19-Mar-18 12:58 Refresh 1