Question

The conjugation 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 $\frac{-1}{i+1}$

$\overline{z}=\frac{1}{i-1}$ Now, $z=\overline{\overline{z}}$

$⟹z=\frac{1}{-1-i}=\frac{-1}{1+i}$