Question

If `(4+i)/(2-3i) = x+iy` for real numbers `x, y`, then what are `x` and `y` ?

Answer 1

`x=5/13" "` and `" "y=14/13`

Explanation:

`x+iy = (4+i)/(2-3i)`

`color(white)(x+iy) = ((4+i)(2+3i))/((2-3i)(2+3i))`

`color(white)(x+iy) = (8+12i+2i+3i^2)/(2^2-(3i)^2)`

`color(white)(x+iy) = (5+14i)/(4+9)`

`color(white)(x+iy) = (5+14i)/13`

`color(white)(x+iy) = 5/13+14/13i`

So `x=5/13" "` and `" "y=14/13`