For the complex number Z, the sum of all the solutions of Z^2+Z=Z¯^2 is equal to

Correct answer: 0. Z^2+Z=Z¯^2 … 1 Taking conjugate, Z¯^2+Z=Z^2 … 2 Adding 1 & 2, we get, ⇒2Z=0 ⇒Z=0

Q6 / 108 · NTA Abhyas (JEE Main) 2020 · Mathematics · Complex Number

For the complex number $Z$ , the sum of all the solutions of $Z^{2} + |Z| = {(\bar{Z})}^{2}$ is equal to

Correct answer: 0

Z^{2} + |Z| = {(\bar{Z})}^{2}

…

(1)

Taking conjugate,

{(\bar{Z})}^{2} + |Z| = Z^{2}

…

(2)

Adding

(1)

(2)

, we get,

\Rightarrow 2 |Z| = 0

\Rightarrow Z = 0

Hence, the correct answer is 0.