Find all complex fourth roots of 1 In other words find all c

Find all complex fourth roots of 1. In other words, find all complex solutions of x^4=1. Thank you!

Solution

x⁴=1

x⁴=e⁰ⁱ

x=(e^(0+2k)i)^1/4,k=0,1,2,3

x=e^((/2)k)i,k=0,1,2,3

x=e⁽⁰⁾ⁱ,x=e^(/2)i,x=e⁽⁾ⁱ,x=e^(3/2)i

x=1,x=i,x=-1,x=-i

all roots are 1,i,-1,-i