Select the product \( (4+i)(-2-i) \) in the standard form \( a+b i \). a.) \( -8-i^{2} \) b.) \( 8-i^{2} \) c.) \( 7-6 i \) d.) \( -7-6 i \)

Calculate or simplify the expression \( (4+i)(-2-i) \). Simplify the expression by following steps: - step0: Solution: \(\left(4+i\right)\left(-2-i\right)\) - step1: Apply the distributive property: \(4\left(-2\right)+4\left(-i\right)+i\left(-2\right)+i\left(-i\right)\) - step2: Multiply the numbers: \(-8+4\left(-i\right)+i\left(-2\right)+i\left(-i\right)\) - step3: Multiply the numbers: \(-8-4i+i\left(-2\right)+i\left(-i\right)\) - step4: Multiply the numbers: \(-8-4i-2i+i\left(-i\right)\) - step5: Multiply the numbers: \(-8-4i-2i+1\) - step6: Calculate: \(-7-4i-2i\) - step7: Multiply the numbers: \(-7-6i\) The product \( (4+i)(-2-i) \) in the standard form \( a+bi \) is \( -7-6i \). Therefore, the correct answer is d.) \( -7-6i \).