AP EAMCET · Maths · Complex Number
For any two non-zero complex numbers \(z_1\) and \(z_2\), if \(\left|z_1+z_2\right|^2=\left|z_1\right|^2+\left|z_2\right|^2\), then
- A \(\operatorname{Re}\left(\frac{z_1}{z_2}\right)=0\)
- B \(\operatorname{Im}\left(\frac{z_1}{z_2}\right)=0\)
- C \(\operatorname{Re}\left(z_1 z_2\right)=0\)
- D \(\operatorname{Im}\left(z_1 z_2\right)=0\)
Answer & Solution
Correct Answer
(A) \(\operatorname{Re}\left(\frac{z_1}{z_2}\right)=0\)
Step-by-step Solution
Detailed explanation
\(\left|z_1+z_2\right|^2 = \left|z_1\right|^2+\left|z_2\right|^2+2\operatorname{Re}(z_1\bar{z_2})\) \(\left|z_1\right|^2+\left|z_2\right|^2 = \left|z_1\right|^2+\left|z_2\right|^2+2\operatorname{Re}(z_1\bar{z_2})\) \(2\operatorname{Re}(z_1\bar{z_2}) = 0\)…
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