Question

find all the eighth roots of (19+7i)

Answer 1

solve
z^8= 19+ 7i

, where z is a complex number

Answer 2

Demouvre?

Answer 3

yes

Answer 4

(that is a hint as well as a question on my part :) thanks @perl)

Answer 5

This is a very useful theorem , which we can use here.

Answer 6

did you know answer of this question

Answer 7

yes

Answer 8

lets start with Demoivre's theorem

Answer 9

please work with perl @vikiy , it is against the code of conduct to just want solutions. We are all here to help, not just give answers

Answer 10

and then you can solve it :)

Answer 11

if anybody wants to post Demoivre's theorem, please don't hesitate

Answer 12

19+7i is a messy number

Answer 13

roughly speaking

( r cos t + i sin t ) ^ (n) = r^n ( cos nt + i sin nt)

Answer 14

so the trick is to get 19 + 7i into r cos t + i sin t , form

Answer 15

r = sqrt( 19^ + 7^2)

t = atan( 19,7)