When a complex number z is written in the polar formz = r(cos θ + i sin θ), the nonnegative number r isthe____ or_____ of z, and the angle θ,0 ≤ θ < 2π, is the______ of z.

When a complex number z is written in the polar formz = r(cos θ + i sin θ), the nonnegative number r isthe__ or_ of z, and the angle θ,0 ≤ θ < 2π, is the____ of z.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.6: De Moivre’s Theorem And Nth Roots Of Complex Numbers

Problem 9E

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Question

When a complex number z is written in the polar form
z = r(cos θ + i sin θ), the nonnegative number r is
the____ or_____ of z, and the angle θ,
0 ≤ θ < 2π, is the______ of z.

Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.

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