Question

Find the conjugate of the following complex number:

\[\frac{1}{1 + i}\]

Answer 1

\[\text {  Let } z = \frac{1}{1 + i}\]

\[ = \frac{1}{1 + i} \times \frac{1 - i}{1 - i}\]

\[ = \frac{1 - i}{1 - i^2}\]

\[ = \frac{1 - i}{2}\]

\[ \Rightarrow \bar{z} = \frac{1 + i}{2}\]