AP EAMCET · Maths · Complex Number
The value of \(|z|^2+|z-3|^2+|z-i|^2\) is minimum when \(z\) equals
- A \(2-\frac{2}{3} i\)
- B \(45+3 i\)
- C \(1+\frac{1}{3} i\)
- D \(1-\frac{1}{3} i\)
Answer & Solution
Correct Answer
(C) \(1+\frac{1}{3} i\)
Step-by-step Solution
Detailed explanation
The expression \(|z|^2+|z-3|^2+|z-i|^2\) is minimized when \(z\) is the centroid of the points \(0, 3, i\). \(z = \frac{0+3+i}{3}\) \(z = 1+\frac{1}{3}i\)
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