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 D

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

Explanation for the correct option:

Finding the complex number:

Given the conjugate is $\frac{1}{(i-1)}$

Let

$$\begin{gathered} z=\frac{1}{i-1} \\ =\frac{1}{-1+i} \end{gathered}$$

To find the conjugate of complex number, replace $i$ with $\left(-i\right)$

The denominator is $-1+i$. Therefore, its conjugate is $-1-i$.

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

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

Thus, the complex number is $\frac{-1}{(i+1)}$

Hence, option (D) is the correct answer.