WBJEE · Maths · Complex Number
The points representing the complex number z for which arg \(\left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}\) lie on
- A a circle
- B a straight line
- C an ellipse
- D a parabola
Answer & Solution
Correct Answer
(A) a circle
Step-by-step Solution
Detailed explanation
Let \(z=x+i y\) \(\therefore \quad \frac{z-2}{z+2}=\frac{x+iy-2}{x+i y+2}\) \(=\frac{(x-2)+i y}{(x+2)+6 y} \times \frac{(x+2)-i y}{(x+2)-i y}\) \(=\frac{(x-2)(x+2)+i y(x+2)-i y(x-2)-i^{2} y^{2}}{(x+2)^{2}-(i y)^{2}}\)…
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