Complex Numbers

The ComplexNumber Class

Source: ComplexNumber.cs

namespace: UniversityPhysics.Maths

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• Properties
• Constructors
• Methods
  • ToPower
• Overrides
  • ToString
• Operators
  • Addition ( + )
  • Subtraction ( - )
  • Multiplication ( * )
  • Division ( / )
  • Equal ( == )
  • Not Equal ( != )

Properties

public double RealPart { get; set; }
public double ImaginaryPart { get; set; }
public double Magnitude { get; }
public double Phase { get; }
public double Conjugate { get; }

Constructors

ComplexNumber(double realPart, double imagPart)

Methods

ToPower()

ComplexNumber ToPower(double p)

Returns the value of this complex number raised to the given value p.

Values raised to the power 0 will return (1 + 0i)

returns: ComplexNumber

ComplexNumber A = new ComplexNumber(1, 2);

ComplexNumber result = A.ToPower(2);

// ===> result = "-3+4i"

ComplexNumber result2 = A.ToPower(0);

// ===> result2 = "1+0i"

ComplexNumber resul3t = A.ToPower(-2);

// ===> result3 = "-3/25 - 4i/25"

Overrides

ToString()

Returns a string representation of the complex number

returns: string

ComplexNumber A = new ComplexNumber(5, 1);

string  s = A.ToString();

// ===> s = "5+1i"

Operators

Addition operator +

Addition of two complex numbers

returns: ComplexNumber

ComplexNumber A = new ComplexNumber(5, 1);
ComplexNumber B = new ComplexNumber(2, 3);

ComplexNumber result = A + B;

// result = Complex Number 7+4i;

You can also add double and int values with a complex number

ComplexNumber A = new ComplexNumber(5, 1);

ComplexNumber result = 5 + A + 2;

// result = Complex Number 12+1i;

Subtraction operator -

Mathematical subtraction of two complex numbers

ComplexNumber A = new ComplexNumber(5, 1);
ComplexNumber B = new ComplexNumber(2, 3);

ComplexNumber result = A - B;

// result = Complex Number 3-2i;

You can also subtract double and int values with a complex number

ComplexNumber A = new ComplexNumber(5, 1);

ComplexNumber result = 5 - A - 2;

// result = Complex Number -2+1i;

Multiplication operator *

Multiplies a complex number by a given numerical value

returns: ComplexNumber

ComplexNumber A = new ComplexNumber(5, 1);
ComplexNumber B = new ComplexNumber(2, 3);

ComplexNumber result = A * B;

// result = Complex Number 7+17i;

You can also multiply double and int values with a complex number

ComplexNumber A = new ComplexNumber(5, 1);

ComplexNumber result = 5.0 * A * 2;

// result = Complex Number 50+10i;

Division operator /

Divides a complex number by a given numerical value

returns: ComplexNumber

ComplexNumber A = new ComplexNumber(5, 1);
ComplexNumber B = new ComplexNumber(2, 3);

ComplexNumber result = A / B;

// result = Complex Number 1-1i;

You can also divide double and int values with a complex number

ComplexNumber A = new ComplexNumber(5, 1);

ComplexNumber result = 1.0 / A / 2;

// result = Complex Number 0.096 - 0.019i;

Equal operator ==

Tests for equality between two complex number

returns: bool

ComplexNumber A = new ComplexNumber(5, 1);
ComplexNumber B = new ComplexNumber(2, 3);

bool result = A == B;

// result = False;

Not Equal operator !=

Tests for numerical inequality between two complex numbers

returns: bool

ComplexNumber A = new ComplexNumber(5, 1);
ComplexNumber B = new ComplexNumber(2, 3);

bool result = A != B;

// result = True;