Solve for x and y (both real):

a) 2x + 3 + (3y-2)i = 4

b) 3 + (x + iy) = 5 + 8i

a)

We have,

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

⇒ 2x + 3 + (3y-2)i = 4 + 0i

On comparing the like terms, we get 

2x + 3  = 4 and 3y - 2 = 0

⇒ 2x = 1 and 3y = 2 

⇒ x = 1/2 and y = 2/3

b) 

We have,

3 + (x + iy) = 5 + 8i

⇒ (3 + x) + iy = 5 + 8i

On comparing the like terms, we get

x + 3 = 5 and y = 8

⇒ x = 2 and y = 8