JEE Mains · Maths · STD 11 - 4.1 complex nubers
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
- A \(\frac{\sqrt{3}}{2}\)
- B \(\frac{2}{\sqrt{3}}\)
- C \(\frac{1}{\sqrt{3}}\)
- D \(2 \sqrt{3}\)
Answer & Solution
Correct Answer
(D) \(2 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Re}(z)=|z-1|\) \(\Rightarrow \quad x=\sqrt{(x-1)^{2}+(y-0)^{2}} \quad(x>0)\) \(\Rightarrow \quad y^{2}=2 x-1=4 \cdot \frac{1}{2}\left(x-\frac{1}{2}\right)\) \(\Rightarrow\) a parabola with focus \((1,0)\) and directrix as imaginary axis. \(\therefore \quad\)…
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