Question

find the multiplicative inverse of 1+i

Answer 1

Your answer !!

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

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Answer 2

Hey there!

We know that, Multiplicative inverse of a is 1/a

So, Now

Multiplicative inverse of 1 + i is 1/ 1 + i

So, We will rationalise it with its simple R. F

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


Therefore, Multiplicative inverse of 1 + i is 1 - i / 2