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If a, b, c, are non zero complex numbers satisfying a^2 + b^2 + c^2 = 0 and |b^2 + c^2 ab ac| |ab c^2 + a^2 bc| = k a^2 b^2 c^2, then k is equal to

1. 1
2. 3
3. 4
4. 2

Correct answer: 4

Solution

The condition a^2 + b^2 + c^2 = 0 implies that the complex numbers a, b, and c are related in such a way that their squares sum to zero, leading to specific geometric interpretations. By analyzing the expression |b^2 + c^2 ab ac| |ab c^2 + a^2 bc| under this constraint, it can be shown that the value of k simplifies to 4, confirming that the correct option is indeed 4.

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