Question

Which of the following expressions is a fourth root of unity?

Answer 1

.__.

Answer 2

forth root of unity is the square root of the square root of unity
and whats the square root of unity ?

Answer 3

-1 ?? :)

Answer 4

so... i ? :o

Answer 5

Right? (:

Answer 6

yes, \(\sqrt{-1}=i\)
and here we are asked 4th root of 1
let that be \(x\).
so, \(x^4 =1 \\x^4-1=0\)
can you factorize this ?

Answer 7

1 .. ? .__.

Answer 8

._O

Answer 9

sorry i lost connection.
to factor, we use \(\large a^2-b^2=(a+b)(a-b)\)
so,
\(x^4-1 =(x^2)^2-1^2= (x^2-1)(x^2+1)=(x+1)(x-1)(x+i)(x-i)=0\)
which gives you,
x+1=0, x=-1
x-1=0,x=1
x+i=0,x=-i
x-i=0,x=i

Answer 10

ask if you have doubt in any step