Answer:
-3 + 18 + i + 5i
Step-by-step explanation:
When adding two imaginary numbers, you proceed to sum up the real terms (the ones without an i) and then the imaginary terms (consider the real terms as like terms and the imaginary ones as like terms) and then you write the answer as a new imaginary number a +bi
The commutative property of addition states that given 2 numbers a and b, you can "switch" them when adding them and you would still get the same result. In other words, order doesn't matter when summing up
a + b = b + a
In this case you have (-3 + i) + (18 + 5i)
First you can get rid of the parentheses and you get:
-3 + i + 18 + 5i
Now, using the commutative property we can switch the i and the 18 so we can later sum up like terms and we get:
-3 + 18 + i + 5i
This expression would demonstrate the use of the commutative property of addition in this first step.
We can group the real terms in parenthesis as
(-3 + 18) + (i + 5i) and this would be your answer in this first step.
Continuing with the sum, as stated above, we said we would sum up the real numbers and the imaginary ones, so we would get
-3 + 18 = 15
i + 5i = 6i
And the final result would be (15 + 6i)
