Question

find the 4th roots of the complex number z(subscript)1=1+sqrt3i.

please help!

Answer 1

arctan(sqrt3/1) = 60 degrees

Answer 2

the length of (1,sqrt3) = 2

Answer 3

therefore:\[2^{1/4}(cos(60/4)+isin(60/4))\]

Answer 4

thats correct bravo

Answer 5

is that the one of the 4 roots? how do i find the other 3?

Answer 6

add multiples of 90 degrees to the angle ... 3 times

Answer 7

yeah

Answer 8

so 4th root of 2 ( cos 105) + i sin(105) is the second one?
and 4th root of 2(cos95) + isin(195) is the third ?
and 4th root of 2(285) + i sin(185) is the fourth one?

Answer 9

(60/4) + 90n, n=0,1,2,3