completely simplify the expression (1 - 2i)(4 + 7i).\na. 18 - i\nb. 4 - 14i\nc. 4 - 15i\nd. -10 - i\ne. 18 + i

Explanation:

Step1: Use FOIL method

$(1 - 2i)(4 + 7i)=1\times4+1\times7i-2i\times4-2i\times7i$

Step2: Calculate each term

$1\times4 = 4$, $1\times7i=7i$, $-2i\times4=-8i$, $-2i\times7i=-14i^{2}$. Since $i^{2}=-1$, then $-14i^{2}=-14\times(-1) = 14$.

Step3: Combine like - terms

$4 + 7i-8i + 14=(4 + 14)+(7i-8i)=18 - i$

Answer:

A. $18 - i$