If the points represented by complex numbers $z_{1}$ = $a + i b$ , $z_{2}$ = $a^{1} + i b^{1}$ and $z_{1} - z_{2}$ are coliinear, then

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Solution

The correct option is B

By definition, $z_{1}$ = $x_{1} + i y_{1}; z_{2}$ = $x_{2} + i y_{2}; z_{3}$ = $x_{3} + i y_{3}$ are collinear, if

$∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣$ = 0 $\Rightarrow$ $∣ ∣ ∣ ∣ \begin{matrix} a & b & 1 a^{'} & b^{'} & 1 a - a^{'} & b - b^{'} & 1 \end{matrix} ∣ ∣ ∣ ∣$ = 0

$\Rightarrow a b^{'}$ = $a^{'} b$

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