Complex Numbers — quick polar / cartesian

VCE Specialist Mathematics · Complex numbers basics · 6 flashcards, free to study.

Just the formulas for Unit 3 complex SACs.

i² = ?

-1

Conjugate of a + bi

a - bi

Modulus of z = a + bi

|z| = √(a² + b²)

Polar form of z

z = r(cosθ + i sinθ) = r cis θ where r = |z|, θ = arg(z)

De Moivre's theorem

(r cis θ)ⁿ = rⁿ cis (nθ)

Multiplying in polar form

|z₁z₂| = |z₁||z₂|; arg(z₁z₂) = arg(z₁) + arg(z₂).

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