Complex Numbers — Formula Sheet

The imaginary unit i is defined by i² = -1

Powers of i follow a cyclic pattern

i¹ = i, i² = -1, i³ = -i, i⁴ = 1

Additive identity

0 = 0 + 0i

Multiplicative identity

1 = 1 + 0i

Modulus of z = x + iy is |z| = √(x² + y²)

The imaginary unit i is defined such that i² = -1.

Addition

(x₁ + iy₁) + (x₂ + iy₂) = (x₁ + x₂) + i(y₁ + y₂).

Subtraction

z₁ - z₂ = (x₁ - x₂) + i(y₁ - y₂).