For simplifying this equation, one thing that needs to be kept in mind is that the value of i^2 is - 1. Noe let us get down to simplifying the equation given.
(1 + 2i) * (5 - 3i) = 1(5 - 3i) + 2i(5 - 3i)
= 5 - 3i + 10i - 6i^2
= 5 + 7i - 6(- 1)
= 5 + 7i + 6
= 7i + 11
The above expression is the simplest form of expression for the equation given in question. I hope the answer helps you.