type the correct answer in the box. simplify the following expression into the form a + bi, where a and b…

Explanation:

Step1: Expand the first - product

Use the FOIL method ((a + b)(c + d)=ac+ad+bc+bd) for ((4 - i)(-3 + 7i)). [ \begin{align*} (4 - i)(-3 + 7i)&=4\times(-3)+4\times7i+(-i)\times(-3)+(-i)\times7i\ &=-12 + 28i+3i-7i^{2}\ &=-12 + 31i + 7\ &=-5+31i \end{align*} ]

Step2: Expand the second - product

[ \begin{align*} 7i(8 + 2i)&=7i\times8+7i\times2i\ &=56i+14i^{2}\ &=56i - 14 \end{align*} ]

Step3: Subtract the second - expanded product from the first

[ \begin{align*} (-5 + 31i)-(56i - 14)&=-5 + 31i-56i + 14\ &=(-5 + 14)+(31i-56i)\ &=9-25i \end{align*} ]

Answer:

(9-25i)