Question

The conjugate of a complex number is $\frac{1}{i-1},$ then that complex number is-

• A. $\frac{-1}{i-1}$
• B. $\frac{1}{i+1}$
• C. $\frac{-1}{i+1}$
• D. $\frac{1}{i-1}$

Answer 1

The correct option is C $\frac{-1}{i+1}$

$\begin{array}{c}z=\frac{1}{i-1}=\frac{1}{-1+i}\\ \therefore \overline{z}=\frac{1}{-1-i}=\frac{-1}{i+1}\end{array}$

Hence, the option $C$ is the required answer.