Question

Find the roots of (z + 1)8 = (z2 − 1)8.

Answer 1

The equation above gives

(z2 − 1) = ei2πn/8 (z + 1), n = 0, 1, 2 · ··, 7 ,

or

(z + 1)(z − 1 − ei2πn/8) = 0, n = 0, 1, 2 · ··, 7.

Thus the roots are

z = −1 and z = 1 + ei2πn/8, n = 0, 1, 2 · ··, 7 .