If the complex numbers $z_{1}, z_{2}, z_{3}$ and $z_{4}$ denote the vertices of a square taken in order. If $z_{1} = 3 + 4 i$ and $z_{3} = 5 + 6 i$ , then the other two vertices $z_{2}$ and $z_{4}$ are respectively

5 + 4 i, 5 + 6 i

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5 + 4 i, 3 + 6 i

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5 + 6 i, 3 + 5 i

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3 + 6 i, 5 + 3 i

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5 + 5 i, 5 + 3 i

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Solution

The correct option is E $5 + 4 i, 3 + 6 i$
Given, $z_{1} = 3 + 4 i$
and $z_{3} = 5 + 6 i$
are two vertices of a square.
$∴$ Mid-point of diagonal
$(z_{0}) = (\frac{3 + 4 i + 5 + 6 i}{2}) = 4 + 5 i$
(since, diagonal of a square bisected each other)
Now by inspection, we get
$z_{2} = 5 + 4 i$ and $z_{4} = 3 + 6 i$
$(∵ z_{0} = \frac{z_{2} + z_{4}}{2} = 4 + 5 i)$ .

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Similar questions

z_{1} = 3 + 2 i, z_{2} = 4 + 4 i, z_{3} = 5 + 6 i,

z_{1}, z_{2}, z_{3}

z_{1} = 5 + 5 i, z_{2} = - 4 + 4 i, z_{3} = - 3 - 3 i

z_{4} = 2 - 2 i,

i = \sqrt{- 1}

z_{1}

z_{2}

z_{1} = 2 + 4 i z_{2} = 5 - 6 i

z_{2} - z_{1}

The value of |(3+4i)+ (5+6i)| is

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

z_{1}, z_{2}

z_{3}

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