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Z = x + iy represents a point in the Argand plane. Find the locus of Z such that |Z| = 2. |
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Answer» Let Z = x + iy. Then |Z| = 2. If and only if |x + iy| = 2. If and only if √(x2 + y2) = 2. If and only if x2 + y2 = 4 x2 + y2 = 4 represents a circle with centre at (0, 0) and radius 2! ∴ The locus of |z| = 2 is the circle x2 + y2 = 4. |
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