Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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**Problem Statement:** Find all \( z \) for which \( z^3 = 8i \). Write them in exponential form. Show the principal cube root.
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Transcribed Image Text:**Problem Statement:** Find all \( z \) for which \( z^3 = 8i \). Write them in exponential form. Show the principal cube root.
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Step 1: Describing the required formula

B y space D e M o i v r e apostrophe s space t h e o r e m comma space w e space k n e w space t h a t space f o r m u l a space f o r space t h e space c u b e space r o o t space o f space t h e space c o m p l e x space n u m b e r space space z space space space i s cube root of z equals cube root of r left parenthesis c o s fraction numerator theta plus 2 k pi over denominator 3 end fraction plus i space s i n fraction numerator theta plus 2 k pi over denominator 3 end fraction right parenthesis space space w h e r e space space k equals 0 comma 1 comma 2.

Here given z=8i

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