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# complex

Let z1, z2, z3 be complex numbers of unit modulus such that Iz1-z2I^2+Iz1-z3I^2=4 then Iz1+z3I is equal to?

Note by Gopal Chpidhary
4 years, 3 months ago

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It doesn't have a unique answer. It should have been mod[z2+z3]. and the answer to that is zero. z1 z2 z3 all lie on circle mod z=1. your condition implies z1 z2 z3 form a right triangle. with z2 and z3 on a diameter and since centre is at 0. z2=-z3 or z2+z3=0. z1+z3 has no meaning

- 4 years, 3 months ago