Complex Numbers Equation?

Question

I just can't understand the topic. No matter how hard I practice I never seem to get it right. And now I have a 20 pts homework about it. I'll give one number, and please explain to me how the process works. And the solution of answer won't hurt either :)

Solve.

(1 + 2i) x + 3 - 2i = 4 - 5 + 3ix

Answer 1

(1 + 2i) x + 3 - 2i = 4 - 5 + 3ix
(1 + 2i) x - 3ix = -3 + 2i + 4 - 5
(1 -i )x = -4 + 2i
x=(-4 + 2i)/(1 -i )
x= -3 - i

Answer 2

Why don't you try isolating x like you'd normally do?

(1+2i - 3i)*x = 4-5-3 + 2i
(1-i)*x = 2i-4
x = (2i-4)/(1-i)

Now you simplify by multiplying numerator and denominator by 1+i
x = (2i-4)*(1+i) / (1-i^2)
= (2i - 4i - 4 + 2i^2) / (1-i^2)

Remember i^2 = -1
x = (-2i-6)/(2)
= -(i+3)

Answer 3

x + 2i x - 3i x = - 1- 3 + 2i
x - i x = - 4 + 2i
(1 - i) x = (- 4 + 2i)
x = (- 4 + 2i) / (1 - i)
x = [ (- 4 + 2i) (1 + i) ] / (1² + 1²)
x = [ - 4 - 2i - 2 ] / 2
x = (- 6 - 2i) / 2
x = - 3 - i