what is the value of (7 + 2i)(3 - i)?\na. 19 - i\nb. 21 - 2i\nc. 21 + i\nd. 23 - i

Answer:

D. $23 - i$

Explanation:

Step1: Use FOIL method

$(7 + 2i)(3 - i)=7\times3+7\times(-i)+2i\times3+2i\times(-i)$

Step2: Calculate each term

$7\times3 = 21$, $7\times(-i)=-7i$, $2i\times3 = 6i$, $2i\times(-i)=-2i^{2}$

Step3: Substitute $i^{2}=-1$

Since $i^{2}=-1$, then $-2i^{2}=-2\times(-1) = 2$

Step4: Combine like - terms

$21-7i + 6i+2=(21 + 2)+(-7i+6i)=23 - i$