If z_1, z_2 and z_3 are three complex numbers such that z_1 = z_2 = z_3 = 1/z_1 + 1/z_2 + 1/z_3 = 1 , then z_1+z_2+z_3 is

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Correct answer: 1. z_1 = z_2 = z_3 = 1 (given) Now z_1=1⇒z1^2=1⇒z_1z_1¯=1 ⇒1z_1=z_1¯ Similarly, 1z_2=z_2¯ & 1z_3=z_3¯ Now 1/z_1 + 1/z_2 + 1/z_3 = 1 ⇒z_1+z_2+z_3¯=1 (∵z_1¯+z_2¯=z_1+z_2¯) and |z_1+z_2+z_3¯|=1 (∵|z_1¯|=|z|) ⇒ z_1 + z_2 + z_3 = 1

If $z_{1} {, z}_{2}$ and $z_{3}$ are three complex numbers such that $|z_{1}| = |z_{2}| = |z_{3}| = |\frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}}| = 1$ , then $|z_{1} + z_{2} + z_{3}|$ is

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If z1, z2 and z3 are three complex numbers such that z 1 = z 2 = z 3 = 1 z 1 + 1 z 2 + 1 z 3 = 1 , then z1+z2+z3 is

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More Complex Number Questions

If $z_{1} {, z}_{2}$ and $z_{3}$ are three complex numbers such that $|z_{1}| = |z_{2}| = |z_{3}| = |\frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}}| = 1$ , then $|z_{1} + z_{2} + z_{3}|$ is