AP EAMCET · Maths · Complex Number
The locus of a point \(z\) satisfying \(|z|^2=\operatorname{Re}(z)\) is a circle with centre
- A \(\left(0, \frac{1}{2}\right)\)
- B \(\left(-\frac{1}{2}, 0\right)\)
- C \(\left(\frac{1}{2}, 0\right)\)
- D \(\left(0,-\frac{1}{2}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{1}{2}, 0\right)\)
Step-by-step Solution
Detailed explanation
Let \(z=x+i y\) \(|z|=\sqrt{x^2+y^2}\) Now, \(|z|^2=\operatorname{Re}(z)\) \(x^2+y^2=x\) \(\Rightarrow \quad x^2+y^2-x=0\) \(g=1 / 2, f=0\) So, centre of circle \(\left(\frac{1}{2}, 0\right)\).
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