4
QuizMultiple Choice

Polar Form of Complex Numbers

Question 4 • *PGHS Precalculus B

Which pair of equations can be used to verify the rectangular form, z = a + bi, and the polar form of a complex number are equivalent?

Answer
A
a = sin(θ) and b = cos(θ)
B
a = cos(θ) and b = sin(θ)
C
a = rsin(θ) and b = rcos(θ)
D
a = rcos(θ) and b = rsin(θ)

Explanation

The polar form is z = r(cos θ + i sin θ). Distributing r gives z = r cos θ + i(r sin θ). Matching this with the rectangular form z = a + bi shows that a = r cos θ and b = r sin θ, which is choice D.

AI-written and checked against the verified answer.

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