Question

Rewrite the following in the form of a+bi:

$(1 + {2i}^{3} )(2 + {3i}^{5} + {4i}^{6} )$

related to the imaginary number
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Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$so \: here \\ given \: complex \: number \: is \\ \\ z = (1 + 2i {}^{3} )(2 + 3i {}^{5} + 4i {}^{6} ) \\ \\ = [1 + 2( - i)][2 +( 3i {}^{4} .i) + (4i {}^{4} .i {}^{2} ) \: ] \\ \\ = (1 - 2i)[2 + 3(1).i + 4(1)( - 1) \: ] \\ \\ = (1 - 2i)(2 + 3i - 4) \\ \\ = (1 - 2i)(3i - 2) \\ \\ = 3i - 2 - 6i {}^{2} + 4i \\ \\ = 7i - 2 - 6( - 1) \\ \\ = 7i - 2 + 6 \\ \\ a + ib = 7i + 4 \\ \\ equating \: real \: parts \: \\ and \: imaginary \: parts \\ \\ we \: have \\ \\ a = 4 \\ b = 7$