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Precalculus · N-CN

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

Any complex number a+bi can be written as r(cos θ + i sin θ) where r = |a+bi| = √(a²+b²) and θ = arctan(b/a) adjusted for quadrant.

PrecalculusCommon Core HSN-CN.B.4N-CNVerified correct ✓

Worked examples

Write the complex number z = -4 - 3i in polar form r(cosθ + i sinθ). Find r = |z|. Round to 4 decimal places.
Answer: 5
Write the complex number z = 2 - 2i in polar form r(cosθ + i sinθ). Find r = |z|. Round to 4 decimal places.
Answer: 2.8284

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