Answered: Find two square roots for the following…

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter6: Equations

Section6.3: Trigonometric Equations Involving Multiple Angles

Problem 85PS

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Question

Find two square roots for the following complex number. Leave your answers in trigonometric form.

4(cos 310° + i sin 310°)

Expert Solution

Given a complex number:

4(cos 310° + i sin 310°)

To Find: Find two square roots for the following complex number.

Note:

$The n^{th} roots of the complex number z = r (cosθ + isinθ) = r cis θ are given by w_{k} = r^{\frac{1}{n}} cis (\frac{θ}{n} + \frac{360^{0}}{n} k) where k = 0, 1, . . ., n - 1$

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