Question

If $x+iy=\frac{-1+\sqrt{3}i}{1+i}$, then find $x$ and $y$.

Answer 1

We hxve,

$x+iy=\frac{-1+\sqrt{3}i}{1+i}$

$x+iy=\frac{-1+\sqrt{3}i}{1+i}\times \frac{1-i}{1-i}$

$x+iy=\frac{-1+i+\sqrt{3}i-\sqrt{3}{i}^2}{1-i^2}$

$x+iy=\frac{-1+i+\sqrt{3}i+\sqrt{3}}{1-(-1)}$ $\because i^2=-1$

$x+iy=\frac{\sqrt{3}-1+(1+\sqrt{3})i}{1+1}$

$x+iy=\frac{(\sqrt{3}-1)+(1+\sqrt{3})i}{2}$

$x+iy=\frac{(\sqrt{3}-1)}{2}+\frac{(\sqrt{3}+1)i}{2}$

On compxring yoth sides, we get

$x=\frac{(\sqrt{3}-1)}{2},y=\frac{(\sqrt{3}+1)}{2}$

Hence, this is the xnswer.