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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let
$S={z\in\mathbb{C}:\left|\frac{z-6i}{z-2i}\right|=1 \text{ and } \left|\frac{z-8+2i}{z+2i}\right|=\frac{3}{5}}$
Then $\sum_{z\in S}|z|^2$ is equal to:
Solution
$\left|\frac{z-6i}{z-2i}\right|=1 \Rightarrow y=4$
$\left|\frac{z-8+2i}{z+2i}\right|=\frac{3}{5}$
$\Rightarrow x^2+y^2-25x+4y+104=0$
Substitute $y=4$
$x=17,; 8$
$z=17+4i,; 8+4i$
$\sum |z|^2 = 17^2+4^2 + 8^2+4^2 = 385$
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