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

1.	Find the roots of (z + 1)8 = (z2 − 1)8.
Answer» The equation above gives (z² − 1) = e^i2πn/8 (z + 1), n = 0, 1, 2 · ··, 7 , or (z + 1)(z − 1 − e^i2πn/8) = 0, n = 0, 1, 2 · ··, 7. Thus the roots are z = −1 and z = 1 + e^i2πn/8, n = 0, 1, 2 · ··, 7 .

Answer»

The equation above gives

(z² − 1) = e^i2πn/8 (z + 1), n = 0, 1, 2 · ··, 7 ,

(z + 1)(z − 1 − e^i2πn/8) = 0, n = 0, 1, 2 · ··, 7.

Thus the roots are

z = −1 and z = 1 + e^i2πn/8, n = 0, 1, 2 · ··, 7 .

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

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