What is the product of 5 - 3i and the conjugate of 3 + 2i

Question

What is the product of 5 - 3i and the conjugate of 3 + 2i

Thank you for your help, mind also showing the work for it? Thank you.

Answer 1

The conjugate of 3+ 2i is 3 - 2i

Thus, we calculate (5 - 3i)(3 - 2i)

Note that i^2 = -1

You can calculate this in two ways:

Method 1:

(5 - 3i)(3 - 2i) = 5(3 - 2i) - 3i(3 - 2i) = 15 - 10i - 9i + 6i^2 = 15 - 6 + (-10 - 9)i = 9 - 19i

Method 2:

Use the foil method:

(5 - 3i)(3 - 2i) = 5*3 + (5 * -2 - 3 * 3)i + (-3i)*(-2i) = 15 - 19i + 6i^2 = 9 - 19i