### Instruction: Simplify $(5-3i)(-4+3i)$.### Response: To simplify a product of two complex numbers, I can use the distributive property and combine like terms.
I write $(5-3i)(-4+3i)$ as $5(-4+3i) - 3i(-4+3i)$.
I distribute the 5 and the -3i to each term in the parentheses.
I get $-20+15i + 12i - 9i^2$.
I remember that $i^2 = -1$, so I can replace it.
I get $-20+15i + 12i + 9$.
I combine the real and imaginary parts separately.