Mathegoras

Complex numbers › The complex plane › Extremes of the modulus

Modulus of a symmetric complex ratio

High school · ●●○○○ 20 pts

Let z1,z2,z3z_1, z_2, z_3 be complex numbers with ∣z1∣=∣z2∣=∣z3∣=1|z_1|=|z_2|=|z_3|=1, and assume z1+z2+z3≠0z_1+z_2+z_3\neq 0. Find ∣z1z2+z2z3+z3z1z1+z2+z3∣\left|\frac{z_{1} z_{2}+z_{2} z_{3}+z_{3} z_{1}}{z_{1}+z_{2}+z_{3}}\right|.

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complex conjugateunit circle