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Complex Numbers

If z 1 =1+2...

Question

If $z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i, p r o v e t h a t t h e n z_{1}, z_{2} a n d z_{3}$ are collinear.

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Solution

We have,
$z_{1} = 1 + 2 i$
$z_{2} = 2 + 3 i$
$z_{3} = 3 + 4 i$

So,
We know that,
Mid point formula using
$z_{2} = \frac{z_{1} + z_{3}}{2}$
$2 + 3 i = \frac{1 + 2 i + 3 + 41}{2}$
$\Rightarrow 2 + 3 i = 2 + 3 i$
Hence, this is the answer.

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