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The three roots of z³ + i*z² + 2i = 0 are plotted in the complex plane. What is the area of the triangle they form?

1. 2
2. (3/2) sqrt(7)
3. (3/4) sqrt(7)
4. sqrt(7)

Correct answer: 2

Solution

z = i is a root; the remaining roots are 1 - i and -1 - i, giving vertices (0,1), (1,-1), (-1,-1) whose triangle has area 2.

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