Question

Find the multiplicative inverse of $(1+i)$.

Answer 1

Finding the multiplicative inverse of the given complex number.

Given $1+i$is a complex number.

The multiplicative inverse of a complex number is the reciprocal of the complex number itself.

$\therefore$The multiplicative inverse of $1+i$is $\frac{1}{1+i}$

$$\begin{gathered} =\frac{1}{(1+i)}\times \frac{1-i}{1-i} \\ =\frac{(1-i)}{(1^2–i^2)} \\ =\frac{1-i}{2} \end{gathered}$$

Hence, the multiplicative inverse of $1+i$is $\frac{1-i}{2}$.