Complex Arithmetic

Complex Number:

Complex Conjugate:

Note that Also

A complex number is real (has no imaginary part) if and only if z = It is imaginary (has no real part) if and only if z =

Modulus of a Complex Number:

The ordinary Euclidean distance of (x, y) to (0, 0) is We also call this number the modulus of the complex number z = x iy and we write

Note that,

The distance from z to w is | Z - W |. We also have the formulas | z ·w | = | z |·| w | and | Re z |  | z | and | Imz |  | z |.