Question

(1+i) (1-i)^-1 find the value of a and b in a+ib
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Answer 1

Hello Mate,

Here is your answer,

We Know,

$(1 + i)(1 - i) \\ \\ = {1}^{2} - {i}^{2} \\ \\ = 1 - ( - 1) \\ \\ = 2 \\ \\( as \: we \: know \: that \: {i}^{2} = - 1)$

$so \\ \\ {((1 + i)(1 - i))}^{ - 1} \\ \\ = \frac{1}{2}$

This is nothing but,

$\frac{1}{2} + i(0)$

So here,

a = $\frac{1}{2}$

b = 0

Hope it helps:)