JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(z_{1}\) and \(z_{2}\) be two complex numbers such that \(\arg \left(\mathrm{z}_{1}-\mathrm{z}_{2}\right)=\frac{\pi}{4}\) and \(\mathrm{z}_{1}, \mathrm{z}_{2}\) satisfy the equation \(|z-3|=\operatorname{Re}(z) .\) Then the imaginary part of \(z_{1}+z_{2}\) is equal to ..... .
- A \(1\)
- B \(2\)
- C \(6\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
\(|z-3|=\operatorname{Re}(z)\) \(\text { let } Z=x=\text { iy }\) \(\Rightarrow(x-3)^{2}+y^{2}=x^{2}\) \(\Rightarrow x^{2}+9-6 x+y^{2}=x^{2}\) \(\Rightarrow y^{2}=6 x-9\) \(\Rightarrow y^{2}=6\left(x-\frac{3}{2}\right)\) \(\Rightarrow \mathrm{z}_{1}\) and \(\mathrm{z}_{2}\) lie…
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