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Question:

(-5 + 7i) + (4 + 9i)
Due to the
Associative Property of Addition, we can drop the parentheses. This is because parentheses are only used to change the order that operations are performed, and addition is not affected by order.
(-5 + 7i) + (4 + 9i) = -5 + 7i + 4 + 9i

-5 + 7i + 4 + 9i
Now, let’s simplify by combining like terms.
But first, let’s define and identify the terms.
Terms are the values, such as variables and numbers, that are separated by operation signs, such as + and -.
In this case, the terms are:
-5
7i
4
9i

So what does it mean to combine like terms?
Like terms are terms with similar variables (such as 1x and 2x). If the number is not a coefficient of a variable, then it is a like term with all the other numbers that aren’t coefficients.

Example:
Let’s say we have terms 1, 2, 1x, and 2x.
1x and 2x have coefficients of 1 and 2 and are attached to the same variable, x.
1 and 2 are not coefficients, they’re just numbers. This makes them like terms.

In this case:
In this case, our terms are -5, 7i, 4, and 9i.
The like terms in this case are -5 and 4, as well as 7i and 9i.
To combine like terms, add the terms that are alike.
-5 + 4 = -1
7i + 9i = 16i
So by combining like terms, we can simplify this expression to -1 + 16i, or 16i – 1.

16i – 1 cannot be simplified further, so this is the answer to (-5 + 7i) + (4 + 9i).