Consider a line $z (i - 1) + ¯ z (i + 1) = 0$ in the argand plane and a point $z_{1} = 2 + 3 i$ then the reflection of $z_{1}$ in the given line is

2 - 3i

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-2+ 3i

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3 + 2i

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-2 -3i

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Solution

The correct option is C 3 + 2i
If z = x + iy then (x+ iy) (i -1) + (x-iy)(i +1) =0
The given line can be written as y = x
Hence reflection of 2+3i is 3 + 2i

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

z^{2} + ¯ ¯ ¯ z = z,

z_{1} + z_{2} + z_{3}

z

i = \sqrt{- 1}

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