How do you find all the real and complex roots of # x^4=1#?

1 Answer
May 5, 2016

Answer:

Real roots of the equation are #1# and #-1#

and complex roots are #i# and #-i#.

Explanation:

As #x^4=1#, #(x^4-1)=0#

Using #a^2-b^2=(a+b)(a-b)# above is equal to

#(x^2+1)(x^2-1)=0#

or #(x^2-i^2)(x^2-1)#, (as #i^2=-1#)

or #(x+i)(x-i)(x+1)(x-1)=0#

Hence real roots of the equation are #1# and #-1#

and complex roots are #i# and #-i#.