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Find all 2 for which 2³=8i exponential form. write them in Show the pricipal cube root.

Find all 2 for which 2³=8i exponential form. write them in Show the pricipal cube root.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
**Problem Statement:** Find all \( z \) for which \( z^3 = 8i \). Write them in exponential form. Show the principal cube root.
Transcribed Image Text:**Problem Statement:** Find all \( z \) for which \( z^3 = 8i \). Write them in exponential form. Show the principal cube root.
Expert Solution
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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