If |z_1| = |z_2|, is it necessary that z_1 = z_2? - Vidyadip

Question

If $|z_1| = |z_2|,$ is it necessary that $z_1 = z_2$?

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Answer

If $|z_1| = |z_2|$ then $z_1$ and $z_2$ are at the same distance from origin.
But if arg $(z_1) \neq$ arg $(z_2),$ then $z_1$ and $z_2$ are different.
So$,$ if $(|z_1| = |z_2|),$ then it is not necessary that $z_1 = z_2$
Consider $z_1 = 3 + 4i$ and $z_2 = 4 + 3i.$

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