Complex number multiplication?

Question

find z such that (4+2i)z=3-2i

Answer 1

(4 + 2i)z = 3 - 2i

Multiply each side  by 4 - 2i 

(4 - 2i)(4 + 2i)z =(4 - 2i)(3 - 2i)

Recall : (a - b)(a + b) = (a² - b²)

(16 - 4i²)z = (12 - 14i + 4i²)

Substitute i² = -1 in the  above equation

(16 - 4(-1))z = (12 - 14i  +4(-1))

20z = 8 - 14i

Divide each side by 20

z = (8 - 14i) / 20.