Question

find x and y if (x+iy) (1+i) = 2-3i
i means ( iota )​

Answer 1

Answer:

The answer is $x=-\dfrac{1}{2},y=-\dfrac{5}{2}$

Step-by-step explanation:

Given

      $(x+iy)(1+i)=2-3i$

  $\Rightarrow x+iy=\dfrac{2-3i}{1+i}$

Rationalize the denominator

  $\Rightarrow x+iy=\dfrac{2-3i}{1+i}\times \dfrac{1-i}{1-i}$

                 $=\dfrac{2-2i-3i+3i^2}{1-i^2}$

                 $=\dfrac{2-5i+3(-1)}{1-(-1)}\boxed{ \because i^2=-1}$

                 $=\dfrac{-1-5i}{2}=-\dfrac{1}{2}-\dfrac{5}{2}i$

$\Rightarrow x=-\dfrac{1}{2},y=-\dfrac{5}{2}$