By the definition, two complex numbers a + bi and c + di are equal if and only if a = c and b = d. See the lesson Complex numbers and arithmetic operations on them in this site, or any textbook on complex numbers. So, if 2x - 3i = 3 + 6yi, then in accordance with this definition, 2x = 3 and -3 = 6y. It implies that x =and y = = .