Question

If z=1- i, find the imaginary part of z⁶​

Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: find : \\ imaginary \: part \: of \: z {}^{6} \\ \\ given \: complex \: number \\ z = 1 - i \\ \\ z {}^{6} = (1 - i) {}^{6} \\ \\ =( \: (1 - i) {}^{2} ) {}^{3} \\ \\ = (1 + i {}^{2} - 2i) {}^{3} \\ \\ = ( - 2i) {}^{3} \\ \\ = - 8i {}^{3} \\ \\ = - 8 \times ( - i) \\ \\ = 8i \\ \\ a + ib= 0 + 8i \\ \\ equating \: real \: and \: imaginary \: parts \\ we \: get \\ \\ a = 0 \: , \: b = 8 \\ \\ hence \: imaginary \: part \: of \: \\ z {}^{6} \: is \: \: 8 \\ when \: z = 1 - i$