Question

Find the values of x and y which satisfy the given equations $(x,y\in R)$ $\frac{x-1}{1+i}+\frac{y-1}{1-i}=i$.

Answer 1

$\frac{x-1}{1+i}+\frac{y-1}{1-i}=c$

$\frac{(x-1)(1-i)+(y-1)(1+i)}{(1+i)(1-i)}=c$

$\frac{x-xi-1+i+y+yi+i-i}{1+1}=i$

$x(1-i)-1+y(1+i)-1=2i$

$x(1-i)+y(1+i)=2+2i$

$x+y+i(-x+y)=2+2i$

By comparing real and complex part we get,

$x+y=2$ & $y-x=2$

$\Rightarrow 2y=4$

$y=2$

so, $x=0$ & $y=2$