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Find the number of complex numbers $z$ such that $|z - 3 - 5i| = 2$ and $|z - 6 - 6i| = 4.$

 Dec 7, 2020
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Geometric approach: The equation |z - 3 - 5i| = 2 represents the line z - 3 - 5i = r*e^(i theta).  The equation |z - 6 - 6i| = 4 represents the line z - 6 - 6i = s*e^(j*theta).  The lines intersect in only one point, so there is only one solution z.

 Dec 7, 2020

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