Question

`(2x+y)+(3x-4y)i=(x-2)+(4y-5)i` Find x and y..?

Answer 1

`x=-21/11,y=-1/11`

Explanation:

We have

`(2x+y)+(3x-4y)i=(x-2)+(4y-5)i`

We know two complex numbers `a+bi` and `c+di` iff `a=c` and `b=d`. So, in this case, we must have

`2x+y=x-2`

`3x-4y=4y-5`

so

`x=-y-2`

`3(-y-2)-4y=-3y-6-4y=-7y-6=4y-5`

so `11y=-1` and `y=-1/11`

Hence, `x=1/11-2=1/11-22/11=-21/11`

We make a quick check:

`2(-21/11)-1/11=-43/11`

`-21/11-2=-21/11-22/11=-43/11`

So, our values of `x` and `y` are correct.