Question:medium
If \( |z_1| = |z_2| = |z_3| = 1 \) and \( z_1 + z_2 + z_3 = \sqrt{2} + i \), then the number \( z_1 \bar{z}_2 + z_2 \bar{z}_3 + z_3 \bar{z}_1 \) is:
If \( |z_1| = |z_2| = |z_3| = 1 \) and \( z_1 + z_2 + z_3 = \sqrt{2} + i \), then the number \( z_1 \bar{z}_2 + z_2 \bar{z}_3 + z_3 \bar{z}_1 \) is:
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When dealing with complex numbers on the unit circle, their conjugates are simply their reciprocals. This property can help simplify expressions involving complex conjugates.
Updated On: Apr 9, 2026
- a positive real number
- a negative real number
- always zero
- a purely imaginary number
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The Correct Option is C
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