Algebra Trig (dealing with complex numbers)?

Question

Find the values of x and y, where x and y are real numbers.

(3x+2y) - y^3 i = 9-27 i

(^3= cubed, i = imaginary number)

Thanks in advance.

Answer 1

3x + 2y = 9
y ³ = 27 so y = 3

3x + 6 = 9
3x = 3
x = 1

x = 1 , y = 3

Answer 2

This is two equations, one for the real part and one for the imaginary:

imaginary: equate the coefficients of i:

-y^3 = -27
y = 3

real: equate real parts:

3x+2(3) = 9
x = 1

How's that?