Mathslive.ie

COMPLEX NUMBERS

Exam Cog
THE BASICS

i = √−1 · i² = −1

z = x + yi

Add: real+real, imag+imag

MULTIPLY & CONJUGATE

Multiply like brackets, i² → −1

Conjugate of x+yi is x−yi

DIVIDE & ARGAND

Divide: times top & bottom by conjugate

Argand: z = x+yi → point (x, y)

MODULUS & EQUALITY

|z| = √(x² + y²)

Equal: real=real, imag=imag

QUADRATICS

Complex roots come in pairs: x±yi

Prove a root: sub in, get 0