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Level 494

Complex Numbers in Polar Form


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r cis θ to Cartesian form
r (cos θ + i sin θ)
r (modulus)
√a² + b²
θ (argument)
tan⁻¹ (b / a) (+ 180° if the real component is negative)
product of complex numbers
z¹ × z² = r₁× r₂cis (θ₁+ θ₂)
reciprocal of complex numbers
1 / z₁= r₁/ r₂cis (θ₁- θ₂)
quotients of complex numbers
z₁/ z₂= r₁/ r₂cis (θ₁- θ₂)
DeMoivre's Theorem
zⁿ = rⁿ cis (n × θ)
nth root of z = r cis θ
z∧1/n = r∧1/n cis (1/n) (θ + 360°k) (where k = 0, 1... n-1)