Complex Number

The Complex Numbers are a Number Set denoted by that extends the Real Numbers via the Imaginary Unit

• is a Vector Space Isomorphism of
• Like , the complex numbers can be represented within the Cartesian Plane.
• is a closed Algebraic Field

Complex numbers are of the form

• where
• where is the Imaginary Unit

Euler's Formula

• Consequence of Euler’s Identity
• Suppose has an angle and has
• The product has angle , and modulus

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Operations

Binary

Addition

Like adding Vectors in

Subtraction

Like subtracting Vectors in

Multiplication

Division

Unary

Real Component Function

Imaginary Component Function

Argument

Complex Conjugate

Reflects across the Real axis.

Magnitude

Also called “Modulus”

The magnitude is the in the figure.