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Complex Numbers

If z1=1+2i,...

Question

If $z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i$ , then $z_{1}, z_{2}$ and $z_{3}$ are collinear.

A

True

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B

False

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Solution

The correct option is A True
Line formula from $z_{3}$ and $z_{1}$
$(y - y_{1}) = \frac{y_{3} - y_{1}}{x_{3} - x_{1}}$ $\times (x - x_{1})$
$⟹ (y - 2) = \frac{(4 - 2) (x - 1)}{3 - 1}$
$⟹ y - 2 = x - 1 ⟹ y = x + 1$
$z_{2} = (2, 3)$
$y = x + 1$ satisfies $z_{2}$ .
Hence $z_{1}, z_{2}$ and $z_{3}$ are collinear.

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z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i,

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State True and False

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