Find values of x and y if, (3x – 7) + 2iy = –5y + (5 + x)i

Consider (3x – 7) + 2iy = –5y + (5 + x)i,

Comparing the coefficients of real and imaginary parts, we get,

3x – 7 = - 5y …… (1)

2y = 5 + x

2y – 5 = x ……. (2)

Put the value of x from (2) in (1) to get,

3(2y - 5) – 7 = - 5y

⇒ 6y – 15 – 7 = - 5y

⇒ 6y + 5y – 22 = 0

⇒ 11y = 22

⇒ y = 2

Put the value of y in (2) to get,

2(2) – 5 = x

⇒ 4 – 5 = x

⇒ - 1 = x

Hence values of x and y are - 1,2.