Question

express i³+i^10-i^5+i^6 in the form a+ib​

Answer 1

Answer:

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Step-by-step explanation:

$so \: here \: \\ z = i {}^{3} + i {}^{10} - i {}^{5} + i {}^{6} \\ \\ we \: know \: that \\ i {}^{2} = 1 \\ i {}^{3} = - i \\ i {}^{4} = 1$

$thus \: then \\ \\ = - i + (i {}^{8} \times i {}^{2} ) - (i {}^{4} \times i) + (i {}^{4} \times i {}^{2} ) \\ \\ = - i +( i {}^{4} \times i {}^{4} \times ( - 1)) - (1 \times i) + (1 \times ( - 1)) \\ \\ = - i + (1 \times 1 \times ( - 1)) - i - 1 \\ \\ = - 2i - 1 - 1 \\ \\ a + ib= - 2i - 2 \\ \\ equating \: real \: and \: imaginary \: parts \\ we \: have \\ \\ a = - 2 \\ b = - 2$