To add complex numbers, add each pair of corresponding like terms.
The types of problems this unit will cover are:
When working with complex numbers, specifically when adding or subtracting, you can think of variable "i" as variable "x". As far as the calculation goes, combining like terms will give you the solution.
Example 1:
Adding: (5 + 3i) + (3 + 2i) can be re-written as (5 + 3x) + (3 + 2x). The addition sign between the parentheses tells you this is an addition problem. Since there are no coefficients infront of either set of parentheses, you can drop the parentheses from the problem and combine like terms.
5 + 3x + 3 + 2x
5 + 3 + 3x + 2x
8 + 5x
8 + 5i *Answer
Notice that the solution 8 + 5x is never written as 5x + 8; not when working with imaginary numbers. When you replace "x" with "i" at the end, the variable term with "i" in it must come second. The constant term always stays as the first answer.
Solve: (7 - 6i) + (4 + 8i)
7 - 6i + 4 + 8i
7 + 4 -6i + 8i
11 + 2i *Answer
Solve: (4 + 5i) + (2 + 5i)
4 + 5i + 2 + 5i
4 + 2 + 5i + 5i
6 + 10i *Answer
Solve: (1 - 3i) + (-6 + 4i)
1 - 3i + -6 + 4i
1 - 6 - 3i + 4i
-5 + 1i
-5 + i *Answer
To subtract complex numbers, subtract corresponding like terms.
The types of problems this unit will cover are:
Solve: (5 + 3i) - (3 + 2i)
5 + 3i - 3 - 2i
5 - 3 + 3i - 2i
2 + 1i
2 + i *Answer
Solve: (7 - 6i) - (4 + 8i)
7 - 6i - 4 - 8i
7 - 4 - 6i - 8i
3 - 14i *Answer
Solve: (5 + 2i) - (6 + 4i)
5 + 2i - 6 - 4i
5 - 6 + 2i - 4i
-1 - 2i *Answer