If |z1| = |z2|, is it necessary that z1 = z2?

Explanation:

Given |z1| = |z2|

If |z1| = |z2| then z1 and z2 are at the same distance from origin.

But if arg (z1) ≠ arg (z2) then z1 and z2 are different.

So, if |z1| = |z2|, then it is not necessary that z1 = z2.

For example: z1 = 3 + 4i and z2 = 4 + 3i

Here |z1| = |z2| = 5 but z1 ≠ z2.

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