If z 1 , z 2 are complex numbers such that Re(z 1 ) = |z 1 – 1|, Re(z 2 ) = |z 2 – 1| and 1 2 arg( ) , 6 z z p – = then 1 2 Im( ) z z + is equal to :

Question:

If $z_{1}, z_{2}$ are complex numbers such that $\operatorname{Re}\left(z_{1}\right)=\left|z_{1}-1\right|$, $\operatorname{Re}\left(z_{2}\right)=\left|z_{2}-1\right|$ and $\arg \left(z_{1}-z_{2}\right)=\frac{\pi}{6}$, then $\operatorname{Im}\left(z_{1}+z_{2}\right)$ is equal to:

  1. $\frac{2}{\sqrt{3}}$

  2. $2 \sqrt{3}$

  3. $\frac{\sqrt{3}}{2}$

  4. $\frac{1}{\sqrt{3}}$


Correct Option: 2

JEE Main Previous Year 1 Question of JEE Main from Mathematics Complex Numbers and Quadratic Equations chapter.
JEE Main Previous Year Sep. 03, 2020 (II)

Solution:

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