How do you find three cube roots of 1?

1 Answer
Jun 26, 2017

Three cube roots of 1 are

1, 1i32 and 1+i32

Explanation:

Let x=31, then x3=1 or

x31=0

or (x1)(x2+x+1)=0

Hence either x=1

or x2+x+1=0 and using quadratic formula

x=1±14×1×12

= 1±32

= 1±i32

Hence three cube roots of 1 are

1, 1i32 and 1+i32