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  4. If the points represented by the complex number z1=a+ib, z2=a'+ib' and z1 -z2 are collinear, then

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Q. If the points represented by the complex number $z_1=a+ib, z_2=a'+ib' $ and $ z_1 -z_2$ are collinear, then

Complex Numbers and Quadratic Equations

Solution:

By the given condition

$\begin{vmatrix}a&b&1\\ a'&b'&1\\ a-a'&b-b'&1\end{vmatrix}=0$

Operate $R_{3} - R_{1} + R_{2}$, we get

$\begin{vmatrix}a&b&1\\ a'&b'&1\\ 0&0&1\end{vmatrix}=0$

$\Rightarrow ab'-a'b=0$