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Precalculus · N-CN

Multiply and Divide Complex Numbers in Polar Form

To multiply: multiply the moduli and add the arguments. To divide: divide the moduli and subtract the arguments.

PrecalculusCommon Core HSN-CN.B.5N-CNVerified correct ✓

Worked examples

Two complex numbers are given in polar form: z₁ = 1(cos 120° + i sin 120°) and z₂ = 3(cos 90° + i sin 90°). Find the argument (angle in degrees) of z₁ · z₂. Round to 4 decimal places.
Answer: 210
Two complex numbers are given in polar form: z₁ = 2(cos 150° + i sin 150°) and z₂ = 2(cos 45° + i sin 45°). Find the argument (angle in degrees) of z₁ · z₂. Round to 4 decimal places.
Answer: 195

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Complex Numbers in Polar Form — r(cos θ + i sin θ)

More Precalculus topics

Complex Numbers in Polar Form — r(cos θ + i sin θ)De Moivre's Theorem — Powers and Roots of Complex NumbersVectors — Components, Addition, and Scalar MultiplicationDot Product of Vectors — Magnitude and Angle Between VectorsMatrix Addition, Subtraction, and Scalar MultiplicationMatrix Multiplication — 2×2 and 2×1 Cases2×2 Matrix Inverse and DeterminantPolynomial Theorems — Rational Root and Fundamental Theorem