Perform the indicated operations an write the result in standard form.
(9+5i)(6-4i)
expand using FOIL
remember i^2 = -1
To perform the indicated operations, we need to multiply the given complex numbers together. We can do this by using the FOIL method, which stands for First, Outer, Inner, Last.
First, we multiply the first terms of each factor:
9 * 6 = 54
Next, we multiply the outer terms of each factor:
9 * (-4i) = -36i
Then, we multiply the inner terms of each factor:
5i * 6 = 30i
Finally, we multiply the last terms of each factor:
5i * (-4i) = -20i^2
Now, we simplify the result. Notice that i^2 is defined as -1, so we can substitute -1 in place of i^2:
-20i^2 = -20(-1) = 20
Putting it all together, we have:
(9 + 5i)(6 - 4i) = 54 + (-36i) + 30i + 20
= 74 - 6i
Therefore, the result in standard form is 74 - 6i.