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Question: If z = 4 + i\(\sqrt{7}\), then value of z<sup>3</sup> – 4z<sup>2</sup> – 9z + 91 equals –...

If z = 4 + i7\sqrt{7}, then value of z3 – 4z2 – 9z + 91 equals –

A

0

B

1

C

–1

D

2

Answer

–1

Explanation

Solution

Sol. (z – 4)2 = i27 = –7 or z2 – 8z + 23 = 0

z3 – 4z2 – 9z + 91 = (z + 4) (z2 – 8z + 23) – 1