simplify: (-1 + 5i)(-3 + 2i)\na -7 - 17i\nb -7 + 17i\nc 7 - 13i\nd -7 + 13i

Explanation:

Step1: Use FOIL method

[ \begin{align*} (-1 + 5i)(-3+2i)&=(-1)\times(-3)+(-1)\times(2i)+(5i)\times(-3)+(5i)\times(2i)\ \end{align*} ]

Step2: Calculate each product

[ \begin{align*} (-1)\times(-3)&=3\ (-1)\times(2i)&=- 2i\ (5i)\times(-3)&=-15i\ (5i)\times(2i)&=10i^{2} \end{align*} ] Since (i^{2}=-1), then (10i^{2} = 10\times(-1)=-10)

Step3: Combine like - terms

[ \begin{align*} 3-2i-15i - 10&=(3 - 10)+(-2i-15i)\ &=-7-17i \end{align*} ]

Answer:

A. (-7 - 17i)