Multiply the complex numbers:
(7+i)(3-i)
To multiply complex numbers, we can use the FOIL method.
First, we multiply the two real numbers:
7 * 3 = 21
Then, we multiply the two complex numbers:
7 * (-i) = -7i
i * 3 = 3i
Finally, we multiply the two imaginary units:
i * (-i) = -i^2
Since i^2 is defined as -1, we have:
-i^2 = -(-1) = 1
Putting it all together, we have:
(7+i)(3-i) = (21 + 3i - 7i + 1)
Simplifying further,
(7+i)(3-i) = (21 - 4i + 1)
(7+i)(3-i) = 22 - 4i
So, the product of the complex numbers (7+i)(3-i) is 22 - 4i.