Provides a complex data type and common complex calculations. More...

Public Member Functions
	Complex (double real, double img)
	Initialize a new instance of the Complex type using the specified real and imaginary values More...

override bool	Equals (object obj)

override int	GetHashCode ()

bool	isInfinity ()
	Check if a complex number has infinite value More...

bool	isNaN ()
	Check if a complex number has a value that is not a number More...

double	Magnitude ()
	Returns the magnitude (abs) of a complex number More...

double	Phase ()
	Returns the phase of a complex number in radians More...

double	Power ()
	Returns the power (absolute square) of a complex number More...

override string	ToString ()
	Converts the value of a complex number to its equivalent string representation in Cartesian form More...

Static Public Member Functions
static Complex	Acos (Complex c)
	Returns the angle whose cosine is a complex number More...

static Complex	Acosh (Complex c)
	Returns the angle whose hyperbolic cosine is a complex number More...

static Complex	Asin (Complex c)
	Returns the angle whose sine is a complex number More...

static Complex	Asinh (Complex c)
	Returns the angle whose hyperbolic sine is a complex number More...

static Complex	Atan (Complex c)
	Returns the tangent of a complex number More...

static Complex	Atanh (Complex c)
	Returns the angle whose hyperbolic tangent is a complex number More...

static Complex	Conjugate (Complex c)
	Returns the complex conjugate of a complex number More...

static Complex	Cos (Complex c)
	Returns the cosine of a complex number More...

static Complex	Cosh (Complex c)
	Returns the hyperbolic cosine of a complex number More...

static Complex	Ln (Complex c)
	Returns the natural (base e) logarithm of a complex number More...

static Complex	Log (Complex c, double a)
	Returns the logarithm of a complex number on the specified real base More...

static Complex	Log (Complex c, Complex a)
	Returns the logarithm of a complex number More...

static Complex	Log10 (Complex c)
	Returns the base 10 logarithm of a complex number More...

static implicit	operator Complex (double value)
	Implicit operator to assign the specified real value with zero imaginary part More...

static bool	operator!= (Complex A, Complex B)
	Inequality check of two complex numbers More...

static Complex	operator* (Complex A, Complex B)
	Multiplies two complex numbers More...

static Complex	operator+ (Complex A, Complex B)
	Adds two complex numbers More...

static Complex	operator- (Complex A, Complex B)
	Subtracts a complex number from another complex number More...

static Complex	operator- (Complex A)
	Negates (opposite) a complex number More...

static Complex	operator/ (Complex A, Complex B)
	Divides a complex number by another complex number More...

static bool	operator== (Complex A, Complex B)
	Equality check of two complex numbers More...

static Complex	PolarToRec (double magnitude, double phase)
	Polar-to-rectangular conversion More...

static Complex	Pow (Complex c, double a)
	Returns the complex number raised to the specified power More...

static Complex	Reciprocal (Complex c)
	Returns the inverse of a complex number More...

static Complex	Round (Complex c, int decimals)
	Rounds a complex number to the specified number of fractional digits More...

static Complex	Sin (Complex c)
	Returns the sine of a complex number More...

static Complex	Sinh (Complex c)
	Returns the hyperbolic sine of a complex number More...

static Complex	Sqrt (Complex c)
	Returns the square root of a complex number More...

static Complex	Tan (Complex c)
	Returns the tangent of a complex number More...

static Complex	Tanh (Complex c)
	Returns the hyperbolic tangent of a complex number More...

Properties
double	Img `[get, set]`
	Gets or sets the imaginary component of the complex number More...

double	Real `[get, set]`
	Gets or sets the real component of the complex number More...

Detailed Description

Provides a complex data type and common complex calculations.

Constructor & Destructor Documentation

◆ Complex()

dsp.Complex.Complex	(	double	real,
		double	img
	)

Initialize a new instance of the Complex type using the specified real and imaginary values

If no parameters given, returns a complex number with a zero value (0+0i)

Parameters

real	real part of complex number
img	imaginary part of complex number

Returns

Example
The following example instantiates one complex number (c1) and assigns its value to another complex number (c2).

Complex c1 = new Complex(2.534, -4.895);
Complex c2 = c1;
c2.Real = 10;
Console.WriteLine(c1);
Console.WriteLine(c2);

2.534-4.895i

10-4.895i

Member Function Documentation

◆ Acos()

static Complex dsp.Complex.Acos ( Complex c )

static

Returns the angle whose cosine is a complex number

Parameters

c	complex number

Returns: $C=\arccos(c)=-i\ln(c+i\sqrt{1-c^2})$

Example

Complex c = new Complex(1, -1);
c = Complex.Acos(c);
Console.WriteLine(c);

0.904556894302382+1.06127506190504i

◆ Acosh()

static Complex dsp.Complex.Acosh ( Complex c )

static

Returns the angle whose hyperbolic cosine is a complex number

Parameters

c	complex number

Returns: $\displaystyle C=arccosh(c)=\ln(c+\sqrt{c^2-1})$

Example

Complex c = new Complex(1, -1);
c = Complex.Acosh(c);
Console.WriteLine(c);

-1.06127506190504-2.23703575928741i

◆ Asin()

static Complex dsp.Complex.Asin ( Complex c )

static

Returns the angle whose sine is a complex number

Parameters

c	complex number

Returns: $C=\arcsin(c)=-i\ln(ic+\sqrt{1-c^2})$

Example

Complex c = new Complex(1, -1);
c = Complex.Asin(c);
Console.WriteLine(c);

0.666239432492515-1.06127506190504i

◆ Asinh()

static Complex dsp.Complex.Asinh ( Complex c )

static

Returns the angle whose hyperbolic sine is a complex number

Parameters

c	complex number

Returns: $\displaystyle C=arcsinh(c)=\ln(c+\sqrt{c^2+1})$

Example

Complex c = new Complex(1, -1);
c = Complex.Asinh(c);
Console.WriteLine(c);

-1.06127506190504+0.666239432492515i

◆ Atan()

static Complex dsp.Complex.Atan ( Complex c )

static

Returns the tangent of a complex number

Parameters

c	complex number

Returns: $\displaystyle C=\arctan(c)=\frac{i}{2}\ln\left(\frac{i+c}{i-c}\right)$

Example

Complex c = new Complex(1, -1);
c = Complex.Atan(c);
Console.WriteLine(c);

1.01722196789785-0.402359478108525i

◆ Atanh()

static Complex dsp.Complex.Atanh ( Complex c )

static

Returns the angle whose hyperbolic tangent is a complex number

Parameters

c	complex number

Returns: $\displaystyle C=arctanh(c)=\frac{1}{2}\ln\left(\frac{1+c}{1-c}\right)$

Example

Complex c = new Complex(1, -1);
c = Complex.Atanh(c);
Console.WriteLine(c);

-0.402359478108525+1.01722196789785i

◆ Conjugate()

static Complex dsp.Complex.Conjugate ( Complex c )

static

Returns the complex conjugate of a complex number

Parameters

c	complex number

Returns: $C=\overline{c}$

Example

Complex c = new Complex(3, -1);
c = Complex.Conjugate(c);
Console.WriteLine(c);

3+1i

◆ Cos()

static Complex dsp.Complex.Cos ( Complex c )

static

Returns the cosine of a complex number

Parameters

c	complex number

Returns: $C=\cos(a+bi)=\cos(a)\cosh(b)-i\sin(a)\sinh(b)$

Example

Complex c = new Complex(1, -1);
c = Complex.Cos(c);
Console.WriteLine(c);

0.833730025131149+0.988897705762865i

◆ Cosh()

static Complex dsp.Complex.Cosh ( Complex c )

static

Returns the hyperbolic cosine of a complex number

Parameters

c	complex number

Returns: $\displaystyle C=\cosh(a+bi)=\cosh(a)\cos(b)+i\sinh(a)\sin(b)$

Example

Complex c = new Complex(1, -1);
c = Complex.Cosh(c);
Console.WriteLine(c);

0.833730025131149-0.988897705762865i

◆ Equals()

override bool dsp.Complex.Equals ( object obj )

◆ GetHashCode()

override int dsp.Complex.GetHashCode ( )

◆ isInfinity()

bool dsp.Complex.isInfinity ( )

Check if a complex number has infinite value

Returns: Returns true if real or imaginary part of the complex number evaluates to positive or negative infinity.

Example

Complex c = new Complex(25.5, double.NegativeInfinity);

Console.WriteLine(c.isInfinity());

True

◆ isNaN()

bool dsp.Complex.isNaN ( )

Check if a complex number has a value that is not a number

Returns: Returns true if real or imaginary part of the complex number evaluates to a value that is not a number

Example

Complex c = new Complex(25.5, double.NaN);

Console.WriteLine(c.isNaN());

True

◆ Ln()

static Complex dsp.Complex.Ln ( Complex c )

static

Returns the natural (base e) logarithm of a complex number

Parameters

c	complex number

Returns: $C=\ln(c)$

Example

Complex c = new Complex(-2, -1.5);
c = Complex.Ln(c);
Console.WriteLine(c);

0.916290731874155-2.49809154479651i

◆ Log() [1/2]

static Complex dsp.Complex.Log	(	Complex	c,
		double	a
	)

static

Returns the logarithm of a complex number on the specified real base

Parameters

c	complex number
a	logarithmic base (real number)

Returns: $C=\log_{a}(c)$

Example

Complex c = new Complex(-2, -1.5);
c = Complex.Log(c, 2);
Console.WriteLine(c);

1.32192809488736-3.60398428336457i

◆ Log() [2/2]

static Complex dsp.Complex.Log	(	Complex	c,
		Complex	a
	)

static

Returns the logarithm of a complex number

Parameters

c	complex number
a	logarithmic base (real number)

Returns: $C=\log_{a}(c)$

Example

Complex c = new Complex(2, -1.5);
c = Complex.Log(c, new Complex(4,2));
Console.WriteLine(c);

0.436889006331612-0.564845970680781i

◆ Log10()

static Complex dsp.Complex.Log10 ( Complex c )

static

Returns the base 10 logarithm of a complex number

Parameters

c	complex number

Returns: $C=\log_{10}(c)$

Example

Complex c = new Complex(-2, -1.5);
c = Complex.Log10(c);
Console.WriteLine(c);

0.397940008672038-1.08490737319429i

◆ Magnitude()

double dsp.Complex.Magnitude ( )

Returns the magnitude (abs) of a complex number

Returns: $|c|=\sqrt{\Re^2+\Im^2}$

Example

Complex c = new Complex(25.5, 42);

Console.WriteLine(c.Magnitude());

49.1350180624776

◆ operator Complex()

static implicit dsp.Complex.operator Complex ( double value )

static

Implicit operator to assign the specified real value with zero imaginary part

Parameters

value real value

Example

Complex c = 3;

Console.WriteLine(c);

3+0i

◆ operator!=()

static bool dsp.Complex.operator!=	(	Complex	A,
		Complex	B
	)

static

Inequality check of two complex numbers

Parameters

A	complex number
B	complex number

Returns: $true \iff A \ne B$

Example

Complex c1 = new Complex(-5.6, 4.7);
Complex c2 = new Complex(5.6, 4.7);
Console.WriteLine(c1 != c2);

True

◆ operator*()

static Complex dsp.Complex.operator*	(	Complex	A,
		Complex	B
	)

static

Multiplies two complex numbers

Parameters

A	complex number
B	complex number

Returns: $C=A \times B$

Example

Complex c1 = new Complex(21.522, 1.545);
Complex c2 = new Complex(2.421, 324.23);
Complex c3 = c1 * c2;
Console.WriteLine(c3);

-448.830588+6981.818505i

◆ operator+()

static Complex dsp.Complex.operator+	(	Complex	A,
		Complex	B
	)

static

Adds two complex numbers

Parameters

A	complex number
B	complex number

Returns

Example

Complex c1 = new Complex(21.522, 1.545);
Complex c2 = new Complex(2.421, 324.23);
Complex c3 = c1 + c2;
Console.WriteLine(c3);

23.943+325.775i

◆ operator-() [1/2]

static Complex dsp.Complex.operator-	(	Complex	A,
		Complex	B
	)

static

Subtracts a complex number from another complex number

Parameters

A	complex number
B	complex number

Returns

Example

Complex c1 = new Complex(21.522, 1.545);
Complex c2 = new Complex(2.421, 324.23);
Complex c3 = c1 - c2;
Console.WriteLine(c3);

19.101-322.685i

◆ operator-() [2/2]

static Complex dsp.Complex.operator- ( Complex A )

static

Negates (opposite) a complex number

Reverses the sign of both the real and imaginary parts of a complex number.

Parameters

A	complex number

Returns: $C=-1 \times A$

Example

Complex c1 = new Complex(-2, 4);

Console.WriteLine(c1);

2-4i

◆ operator/()

static Complex dsp.Complex.operator/	(	Complex	A,
		Complex	B
	)

static

Divides a complex number by another complex number

Parameters

A	complex number (dividend)
B	complex number (divisor)

Returns: $\displaystyle C=\frac{A}{B}$

Example

Complex c1 = new Complex(21.522, 1.545);
Complex c2 = new Complex(2.421, 324.23);
Complex c3 = c1 / c2;
Console.WriteLine(c3);

0.00526048789834316-0.0663395255182991i

◆ operator==()

static bool dsp.Complex.operator==	(	Complex	A,
		Complex	B
	)

static

Equality check of two complex numbers

Parameters

A	complex number
B	complex number

Returns: $true \iff A=B$

Example

Complex c1 = new Complex(-5.6, 4.7);
Complex c2 = new Complex(5.6, 4.7);
Console.WriteLine(c1 == c2);

False

◆ Phase()

double dsp.Complex.Phase ( )

Returns the phase of a complex number in radians

Returns: $\displaystyle \Theta=\arctan\left(\frac{\Re}{\Im}\right), -\pi\leq\theta\leq\pi$

Example

Complex c = new Complex(25.5, 42);

Console.WriteLine(c.Phase());

1.0251412722679

◆ PolarToRec()

static Complex dsp.Complex.PolarToRec	(	double	magnitude,
		double	phase
	)

static

Polar-to-rectangular conversion

Creates a complex number from polar coordinates

Parameters

magnitude	magnitude of the complex number
phase	phase of the complex number in radians

Returns: $C=\Re+\Im \\ \Re=M\cos(\theta) , \Im=M\sin(\theta)$

Example

Complex c = Complex.PolarToRec(15, 0.7854);

Console.WriteLine(c);

10.6065822376685+10.6066211978921i

◆ Pow()

static Complex dsp.Complex.Pow	(	Complex	c,
		double	a
	)

static

Returns the complex number raised to the specified power

Parameters

c	complex number
a	exponent (real number)

Returns

Example

Complex c = new Complex(3, -1);
c = Complex.Pow(c);
Console.WriteLine(c);

8-6i

◆ Power()

double dsp.Complex.Power ( )

Returns the power (absolute square) of a complex number

Returns: $|c|^2={\Re^2+\Im^2}$

Example

Complex c = new Complex(25.5, 42);

Console.WriteLine(c.Power());

2414.25

◆ Reciprocal()

static Complex dsp.Complex.Reciprocal ( Complex c )

static

Returns the inverse of a complex number

Parameters

c	complex number

Returns: $C=c^{-1}$

Example

Complex c = new Complex(3, -1);
c = Complex.Reciprocal(c);
Console.WriteLine(c);

0.3+0.1i

◆ Round()

static Complex dsp.Complex.Round	(	Complex	c,
		int	decimals
	)

static

Rounds a complex number to the specified number of fractional digits

Rounding applies on both real and imaginary components of the complex number using an away from zero mode.

Parameters

c	complex number
decimals	number of fractional digits

Example

Complex c = new Complex(-1, 1);
c = Complex.Pow(c, 2);
Console.WriteLine(c);
c = Complex.Round(c, 8);
Console.WriteLine(c);

-3.67381906146713E-16-2i

0-2i

◆ Sin()

static Complex dsp.Complex.Sin ( Complex c )

static

Returns the sine of a complex number

Parameters

c	complex number

Returns: $C=\sin(a+bi)=\sin(a)\cosh(b)+i\cos(a)\sinh(b)$

Example

Complex c = new Complex(1, -1);
c = Complex.Sin(c);
Console.WriteLine(c);

1.29845758141598-0.634963914784736i

◆ Sinh()

static Complex dsp.Complex.Sinh ( Complex c )

static

Returns the hyperbolic sine of a complex number

Parameters

c	complex number

Returns: $\displaystyle C=\sinh(a+bi)=\sinh(a)\cos(b)+i\cosh(a)\sin(b)$

Example

Complex c = new Complex(1, -1);
c = Complex.Sinh(c);
Console.WriteLine(c);

0.634963914784736-1.29845758141598i

◆ Sqrt()

static Complex dsp.Complex.Sqrt ( Complex c )

static

Returns the square root of a complex number

Parameters

c	complex number

Returns: $C=\sqrt{c}$

Example

Complex c = new Complex(2, -1);
c = Complex.Sqrt(c);
Console.WriteLine(c);

1.45534669022535-0.343560749722512i

◆ Tan()

static Complex dsp.Complex.Tan ( Complex c )

static

Returns the tangent of a complex number

Parameters

c	complex number

Returns: $\displaystyle C=\tan(c)=\frac{\sin(c)}{\cos(c)}$

Example

Complex c = new Complex(1, -1);
c = Complex.Tan(c);
Console.WriteLine(c);

0.271752585319512-1.08392332733869i

◆ Tanh()

static Complex dsp.Complex.Tanh ( Complex c )

static

Returns the hyperbolic tangent of a complex number

Parameters

c	complex number

Returns: $\displaystyle C=\tanh(c)=\frac{\sinh(c)}{\cosh(c)}$

Example

Complex c = new Complex(1, -1);
c = Complex.Tanh(c);
Console.WriteLine(c);

1.08392332733869-0.271752585319512i

◆ ToString()

override string dsp.Complex.ToString ( )

Converts the value of a complex number to its equivalent string representation in Cartesian form

Example

Complex c = new Complex(3, 1);

Console.WriteLine(c);;

3+1i

Property Documentation

◆ Img

double dsp.Complex.Img

getset

Gets or sets the imaginary component of the complex number

Returns: $\Im$

Example

Complex c1 = new Complex(2.534, -4.895);
Console.WriteLine(c1.Img);
c1.Img = 10;
Console.WriteLine(c1.Img);

-4.895

10

◆ Real

double dsp.Complex.Real

getset

Gets or sets the real component of the complex number

Returns: $\Re$

Example

Complex c1 = new Complex(2.534, -4.895);
Console.WriteLine(c1.Real);
c1.Real = 10;
Console.WriteLine(c1.Real);

2.534

10

Public Member Functions

Static Public Member Functions

Properties

Detailed Description

Constructor & Destructor Documentation

◆ Complex()

Member Function Documentation

◆ Acos()

◆ Acosh()

◆ Asin()

◆ Asinh()

◆ Atan()

◆ Atanh()

◆ Conjugate()

◆ Cos()

◆ Cosh()

◆ Equals()

◆ GetHashCode()

◆ isInfinity()

◆ isNaN()

◆ Ln()

◆ Log() [1/2]

◆ Log() [2/2]

◆ Log10()

◆ Magnitude()

◆ operator Complex()

◆ operator!=()

◆ operator*()

◆ operator+()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator/()

◆ operator==()

◆ Phase()

◆ PolarToRec()

◆ Pow()

◆ Power()

◆ Reciprocal()

◆ Round()

◆ Sin()

◆ Sinh()

◆ Sqrt()

◆ Tan()

◆ Tanh()

◆ ToString()

Property Documentation

◆ Img

◆ Real