1. Tardigrade
  2. Question
  3. Mathematics
  4. Let z 1, z 2 and z 3 be complex numbers such that | z 1|=| z 2|=| z 3|=| z 1+ z 2+ z 3|=2. If | z 1- z 2|= |z1-z3| and z2 ≠ z3. Then find the value of |z1+z2||z1+z3|.

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Q. Let $z _1, z _2$ and $z _3$ be complex numbers such that $\left| z _1\right|=\left| z _2\right|=\left| z _3\right|=\left| z _1+ z _2+ z _3\right|=2$. If $\left| z _1- z _2\right|=$ $\left|z_1-z_3\right|$ and $z_2 \neq z_3$. Then find the value of $\left|z_1+z_2\right|\left|z_1+z_3\right|$.

Complex Numbers and Quadratic Equations

Solution:

The triangle has cirumcentre at origin and its orthocentre lying on the circumcircle.

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