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 A $\frac{-1}{i+1}$

Let $z=\frac{1}{i-1}$

$=\frac{1}{i-1}.\frac{i+1}{i+1}=\frac{i+1}{-2}$

$\therefore \overline{z}=\frac{1-i}{-2}$

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

$=-\frac{1}{i+1}$