Question

What are the complex 5th roots of 5-5√3i?

Answer 1

write in trig form first

Answer 2

you know how to do that?

Answer 3

Ummm. 10(cos60 - isin(60)

Answer 4

not sure about the 10 l

Answer 5

\[\sqrt{5^2+(5\sqrt3)^2}\]

Answer 6

oh you win 10
but there is a mistake there

Answer 7

it should be
\[10\left(\cos(\theta)+i\sin(\theta)\right)\] not minus

Answer 8

Gotcha

Answer 9

angle is not 60

Answer 10

dang draw tool is not working
if you can draw it you will you are in quadrant 4, not 1

Answer 11

Would it be... 300?

Answer 12

yeah i guess
if you are working in degrees

Answer 13

now you want the fifth roots
take \(\sqrt[5]{10}\) as the modulus, and divide the angle by 5
so the first answer will be
\[\sqrt[5]{10}\left(\cos(60)+i\sin(60)\right)\]

Answer 14

Okay...

Answer 15

What about the other four?

Answer 16

one way to do it is to divide the circle up in to five equal parts, with \(60\) degrees as one of them
the other way is to keep adding 360 to the angle and divide by 5 again
\[660\div 5=132\] so the next one is \[\sqrt[5]{10}\left(\cos(132)+i\sin(132)\right)\]

Answer 17

lather, rinse, repeat

Answer 18

Gotcha. Thanks!