Find all real numbers x and y

Question

so I'm a bit confused with the y solution
-2x-4+2yi=3x-2i
2yi=5x-2i+4
I know the answer is
y = -5ix/2 - 2i - 1
so y = -1

But how do you go from
2yi = 5x - 2i + 4 to
y = -5ix/2 - 2i - 1

Answer 1

the real and imaginary parts must be equal, so

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

-2x-4 = 3x
2y = -2

x = -4/5
y = -1

as for your question, recall that since i^2 = -1, 1/i = -i

Dividing through by 2i yields the desired result.

Note also that since x = -4/5,

-5i(-4/5)/2 - 2i - 1
= 2i-2i-1
= -1
which is the solution for y.

Answer 2

2yi = 5x - 2i + 4
Divide everything by 2i to get y alone:
2yi / 21 = (5x - 2i + 4) / 2i
y = (5/2i)x - 1 + 2/i

Hm, I think there's a typo..

Answer 3

^No, I'm sorry don't mind my post ^^;