Modulus-Argument Form (Edexcel A-Level Further Mathematics): Flashcards

$z = r(\cos \theta + i \sin \theta)$

Distance from origin to point

Angle with positive real axis

Polar form

$r = \sqrt{a^2 + b^2}$

$\theta = \tan^{-1}(b/a)$ (adjust for quadrant)

$\cos \theta + i \sin \theta$

Multiply moduli, add arguments

Divide moduli, subtract arguments

Simplifies multiplication and division