SOLUTION: (2-3i)-(4-5i)+(-3+2i)

Question 400985: (2-3i)-(4-5i)+(-3+2i)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
(2-3i) - (4-5i) + (-3+2i)
For many reasons it is a good idea to change any subtractions to additions of the opposite:

Addition is easier than subtraction.
Addition is Commutative so the order can be changed in any desired way.
Addition is Associative so the grouping can be changed in any desired way.
Most "forms" are written in terms of addition:
- Slope-intercept form (of the equation of a line): y = mx + b
- Standard form (of the euqation of a line): Ax + By = C
- Complex numbers: a + bi
- Quadratic equations:
- etc.

Rewriting the subtractions as additions of the opposite we get:
(2+(-3i)) - (4+(-5i)) + (-3+2i)
(2+(-3i)) + (-4+5i)) + (-3+2i)
Only like terms can be added. So we will rearrange the order and the grouping so that all the like terms are grouped:
(2+(-4)+(-3)) + (-3i+5i+2i)
Adding we get:
-5 + 4i
And we are finished.
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