which expression is equivalent to (4 + 7i)(3 + 4i)?\n-16 + 37i\n12 - 28i\n16 - 37i\n37 + 16i

Explanation:

Step1: Use FOIL method

$(4 + 7i)(3 + 4i)=4\times3+4\times4i+7i\times3+7i\times4i$

Step2: Calculate each product

$4\times3 = 12$, $4\times4i=16i$, $7i\times3 = 21i$, $7i\times4i=28i^{2}$ Since $i^{2}=- 1$, then $28i^{2}=-28$

Step3: Combine like - terms

$12+16i + 21i-28=(12 - 28)+(16i+21i)=-16 + 37i$

Answer:

A. $-16 + 37i$