# Simple Complex Number Question (Roots of 1)

## Homework Statement

So on one of my homework assignments I had to find the complex fifth roots of one. Because of Euler's equation the arguments are simply 0, 2pi/5,4pi/5,6pi/5,and 8pi/5. It is easy to see that (e^i2pi/5)^5 = (e^i2pi) = cos(2pi) + isin(2pi) = 1 + 0 = 1 but on my paper I wrote e^(i2pi/5) = 1^(1/5) and similar expressions for all the arguments of the fifth roots and lost 10 point out of 15. I wanted to ask the TA to regrade it but I don't want to bother him if I'm flat out wrong expressing the way I did? Any input would be great.. Thanks!

Dick
Homework Helper

## Homework Statement

So on one of my homework assignments I had to find the complex fifth roots of one. Because of Euler's equation the arguments are simply 0, 2pi/5,4pi/5,6pi/5,and 8pi/5. It is easy to see that (e^i2pi/5)^5 = (e^i2pi) = cos(2pi) + isin(2pi) = 1 + 0 = 1 but on my paper I wrote e^(i2pi/5) = 1^(1/5) and similar expressions for all the arguments of the fifth roots and lost 10 point out of 15. I wanted to ask the TA to regrade it but I don't want to bother him if I'm flat out wrong expressing the way I did? Any input would be great.. Thanks!

## The Attempt at a Solution

Saying e^(i2pi/5) = 1^(1/5) is flat out wrong. 1^(1/5) doesn't mean ANY fifth root of 1. It means 1. Saying (e^(i2pi/5))^5=1 is really what you meant. Still you got the roots. Up to you whether to appeal.

Last edited: