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If $\mid z\mid=2$,then set of points $x+iy=z-\large\frac{1}{z}$ lie on,

(A) Circle

(B) Parabola

(C) Ellipse

(D) Hyperbola

Can you answer this question?
 
 

1 Answer

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$\mid z\mid=2$
$\Rightarrow z=2e^{i\theta}=2(\cos \theta+i\sin \theta)$
$x+iy=z-\large\frac{1}{z}$$=2e^{i\theta}-\large\frac{1}{2e^{i\theta}}$
$\Rightarrow 2e^{i\theta}-\large\frac{1(e^{-i\theta})}{2}$
$\Rightarrow x=\large\frac{3}{2}$$\cos\theta,y=\large\frac{5}{2}$$\sin\theta$
$\Rightarrow \large\frac{x^2}{(9/4)}+\frac{y^2}{(25/4)}$$=1$ which represents an ellipse.
Hence (C) is the correct answer.
answered Apr 9, 2014 by sreemathi.v
 

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