which expression is equivalent to (6 + 2i)(4 - 3i)?\na. 18 - 10i\nb. 24 - 6i\nc. 24 - 16i\nd. 30 - 10i

Explanation:

Step1: Use FOIL method

$(6 + 2i)(4 - 3i)=6\times4+6\times(-3i)+2i\times4+2i\times(-3i)$ $=24-18i + 8i-6i^{2}$

Step2: Recall $i^{2}=-1$

Since $i^{2}=-1$, the expression becomes $24-18i + 8i-6\times(-1)$ $=24-18i + 8i + 6$

Step3: Combine like - terms

Combine the real parts $24 + 6$ and the imaginary parts $-18i+8i$. $(24 + 6)+(-18i + 8i)=30-10i$

Answer:

D. $30 - 10i$