Complex NumbersHard

Question

If z = 2 + 3 i, then the expression z4 - z3 + 10 z2 + 3 z - 5 reduces to a real number equal to:

Options

A.122
B.-122
C.160
D.-160

Solution

z = 2 + 3i ⇒ z2 - 4z + 13 = 0
on dividing the expression by z2 - 4z + 13 we get the remainder (-122)

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