Q. 295.0( 3 Votes )

# If |z_{1}| = |z_{2}|, is it necessary that z_{1} = z_{2}?

Answer :

**Explanation:**

Given |z_{1}| = |z_{2}|

If |z_{1}| = |z_{2}| then z_{1} and z_{2} are at the same distance from origin.

But if arg (z_{1}) ≠ 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}.

For example: z_{1} = 3 + 4i and z_{2} = 4 + 3i

Here |z_{1}| = |z_{2}| = 5 but z_{1} ≠ z_{2}.

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