WBJEE · Maths · Complex Number
If \(z_{1}=2+3 i\) and \(z_{2}=3+4 i\) be two points on the complex plane. Then, the set of complex number \(z\) satisfying \(\left|z-z_{1}\right|^{2}+\left|z-z_{2}\right|^{2}\)
\(=\left|z_{1}-z_{2}\right|^{2}\) represents
- A a straight line
- B a point
- C a circle
- D a pair of straight line
Answer & Solution
Correct Answer
(C) a circle
Step-by-step Solution
Detailed explanation
Given, \(z_{1}=2+3 i\) and \(z_{2}=3+4 i\) Now, we have \(\left|z-z_{1}\right|^{2}+\left|z-z_{2}\right|^{2}=\left|z_{1}-z_{2}\right|^{2}\) (let \(z=x+i y)\) \(\Rightarrow|(x+i y)-(2+3 i)|^{2}+|(x+i y)-(3+4 i)|^{2}\) \(\quad=|(2+3 i)-(3+4 i)|^{2}\)…
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