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If the complex number z satisfies |z + 4| ≤ 3, what is the greatest possible value of |z + 1|?

1. 6
2. 0
3. 4
4. 10

Correct answer: 6

Solution

The inequality |z + 4| ≤ 3 describes a circle in the complex plane centered at -4 with a radius of 3. The farthest point from -1 within this circle occurs at the point on the boundary of the circle that is directly opposite -1, which results in a maximum distance of 6.

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