Find the real values of x and y, if
(x + i y) (2 – 3i) = 4 + i
Given:
⇒ (x+iy)(2-3i)=4+i
⇒ x(2-3i)+iy(2-3i)=4+i
⇒ 2x-3xi+2yi-3yi2=4+i
We know that i2=-1
⇒ 2x+(-3x+2y)i-3y(-1)=4+i
⇒ (2x+3y)+(-3x+2y)=4+i
Equating Real and Imaginary parts on both sides, we get
⇒ 2x+3y=4 and -3x+2y=1
On solving we get,
⇒
∴ The real values of x and y are .