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If the complex number z satisfies z + |z| = 1 + 7i, then find the value of |z|².

1. 625
2. 169
3. 49
4. 25

Correct answer: 625

Solution

With z = x + iy, the imaginary part gives y = 7, and x + sqrt(x² + 49) = 1 yields x = -24, so |z|² = 576 + 49 = 625.

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