**Problem Statement:**Find all $ z $ for which $ z^3 = 8i $. Write them in exponential form. Show the principal cube root.

Answered: Find all 2 for which 2³=8i exponential…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

**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