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10 cards from this deck
z=r(cosθ+isinθ)z = r(\cos \theta + i \sin \theta)z=r(cosθ+isinθ)
Distance from origin to point
Angle with positive real axis
Polar form
r=a2+b2r = \sqrt{a^2 + b^2}r=a2+b2
θ=tan−1(b/a)\theta = \tan^{-1}(b/a)θ=tan−1(b/a) (adjust for quadrant)
cosθ+isinθ\cos \theta + i \sin \thetacosθ+isinθ
Multiply moduli, add arguments
Divide moduli, subtract arguments
Simplifies multiplication and division
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