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For complex numbers z satisfying |z - 25i| <= 15, which point z on this disc has the least positive argument?

1. z = 20 + 15i
2. z = 15 + 20i
3. z = 12 + 16i
4. z = 16 + 12i

Correct answer: z = 20 + 15i

Solution

The minimum-argument point is the tangent point of the line from O to the lower side of the circle. Geometry gives the tangent point z = 20 + 15i.

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