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Complex Numbers

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What is the area of the region of the complex plane defined by |z - 3i| < 8?

Jun 10, 2021

$$|z|<8$$ represents a circle with a radius of 8 centered at (0, 0), and the $$-3i$$ simply shifts that circle upwards by 3 units. Therefore, the area is just the area of a circle with a radius of 8 and should be easily solvable by using the formula $$A=\pi r^2$$, where A is the area of a circle and r is that circle's radius.