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Question: If the conjugate of \((x + iy)(1 - 2i)\) be 1+i, then <img src="https://cdn.pureessence.tech/canvas...

If the conjugate of (x+iy)(1−2i)(x + iy)(1 - 2i) be 1+i, then

A

x=15x = \frac{1}{5}

B

y=35y = \frac{3}{5}

C

x+iy=1−i1−2ix + iy = \frac{1 - i}{1 - 2i}

D

x−iy=1−i1+2ix - iy = \frac{1 - i}{1 + 2i}

Answer

x+iy=1−i1−2ix + iy = \frac{1 - i}{1 - 2i}

Explanation

Solution

Sol. Given that (x+iy)(1−2i)‾=1+i\overline{(x + iy)(1 - 2i)} = 1 + i

⇒x−iy=1+i1+2i⇒x+iy=1−i1−2i\Rightarrow x - iy = \frac{1 + i}{1 + 2i} \Rightarrow x + iy = \frac{1 - i}{1 - 2i}