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Show that |(z -2)/(z - 3)| = 2 represe...

Show that `|(z -2)/(z - 3)| = 2` represents a circle, find its centre and radius.

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To show that \(\left|\frac{z - 2}{z - 3}\right| = 2\) represents a circle and to find its center and radius, we can follow these steps: ### Step 1: Substitute \(z\) Let \(z = x + iy\), where \(x\) and \(y\) are real numbers. Then, we can rewrite the equation: \[ \left|\frac{(x + iy) - 2}{(x + iy) - 3}\right| = 2 \] This simplifies to: ...
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