Theory For z=x+iyz=x+iyz=x+iy: ∣z∣=x2+y2|z|=\sqrt{x^2+y^2}∣z∣=x2+y2 Argument θ\thetaθ is chosen so that: cosθ=x∣z∣,sinθ=y∣z∣\cos\theta=\frac{x}{|z|},\quad \sin\theta=\frac{y}{|z|}cosθ=∣z∣x,sinθ=∣z∣y Polar form: z=∣z∣(cosθ+isinθ)z=|z|(\cos\theta+i\sin\theta)z=∣z∣(cosθ+isinθ) When using tan−1(y/x)\tan^{-1}(y/x)tan−1(y/x), always adjust θ\thetaθ for the correct quadrant.