What is (1-i)^3 Please explain how you got that

1 answer:

6 0

$\bf (1-i)^3\implies ~\hfill \begin{array}{cccccccl} 1^3&+&3(1)^2(-i)^1&+&3(1)^1(i)^2&+&(-i)^3\\\\ 1&+&(-3i)&+&(3i^2)&+&(-i^3)\\\\ 1&-&3i&+&3i^2&-&i^3 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{let's recall that}}{i^2=-1\qquad \qquad i^3=-i} \\\\[-0.35em] ~\dotfill\\\\ 1-3i+3(-1)-(-i)\implies 1-3i-3+i\implies -2-2i$

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Step-by-step explanation:

$given \: expression \: is \\ (5 + 12i) - (9 {i}^{2} - 6i) \: \: \: where \: i = \sqrt{ - 1} \: \: \\ = 5 + 12i - 9 {i }^{2} + 6i \\ = 18i + 5 - 9( - 1) \\ 18i + 5 + 9 \\ = 18i + 14$