Question

The conjugate of a complex number is 1/(i-1). Then the complex number is

Answer 1

Answer:

answer is 1-i/2 is conjugate

Answer 2

Answer- The above question is from the chapter 'Complex Numbers'.

Given question: The conjugate of a complex number is 1/(i-1). Then the complex number is _____ .

Solution: Let z be a complex number.

$\bar{z}$ is its conjugate.

$\bar{z} = \dfrac{1}{i \: - \: 1}\\\\\bar{z} = \dfrac{1}{i \: - \: 1} \times \dfrac{i \: + \: 1}{i \: + \: 1}\\\\\bar{z} = \dfrac{i \: + \: 1}{i^{2} \: - \: 1^{2}}\\\\\bar{z} = \dfrac{i \: + \: 1}{-1 - 1}\\\\\bar{z} = \dfrac{i \: + \: 1}{-2}\\\\\bar{z} = \dfrac{-(i \: + \: 1)}{2}$

$\bar{z} = \dfrac{-1 - i}{2}$

z and $\bar{z}$  are conjugates of each other.

So, if

$\bar{z} = \dfrac{-1 - i}{2}$

then,

$z = \dfrac{-1 + i}{2}$

So, the required complex number is $z = \dfrac{-1 + i}{2}$