Question

What are the fourth roots of i ?

Answer 1

write i^(1/4) as
exp(i pi/2)^(1/4)

they are equispaced about the unit circle, every pi/2 starting at exp(i pi/8)

Answer 2

one way to see this is multiply by exp(i 2pi) (= 1)
(exp(i 2pi)*exp(i pi/2))^(1/4)
to get the next one.
keep multiplying by exp( i n*2pi) and taking the 1/4 root until you start repeating

Answer 3

for n=0 to 3 (n=4 repeats the cycle)

Answer 4

So the first root would be cos(pi/8) + i sin(pi/8), right?

Answer 5

http://answers.yahoo.com/question/index?qid=20110405142837AAJGcPh
go through this link
@estudier

Answer 6

yes

Answer 7

check using (cos x + i sin x)^n = cos nx + i sin nx

Answer 8

Yes, I used deMoivre...

Answer 9

tho it seems more obvious (to me) using exp( i pi/8)^4

Answer 10

it will help you @estudier

Answer 11

I guess it's the same thing.....

Answer 12

yaaa

Answer 13

interesting that the link gives the wrong answer for the 4 roots....

Answer 14

i.e. cos((3pi)/8)+isin((3pi)/8) is the 4th root of -i not +i

Answer 15

right, s/b 5,9 and 13/8.....