Question

the expression to a + bi form: (10 + 8i)(-5 + 6i)

Explanation:

Step1: Apply the distributive property (FOIL method)

We multiply each term in the first complex number by each term in the second complex number.
$$(10 + 8i)(-5 + 6i)=10\times(-5)+10\times6i + 8i\times(-5)+8i\times6i$$

Step2: Simplify each term

• For the first term: $10\times(-5)= - 50$
• For the second term: $10\times6i = 60i$
• For the third term: $8i\times(-5)=-40i$
• For the fourth term: $8i\times6i = 48i^{2}$, and since $i^{2}=-1$, this becomes $48\times(-1)=-48$

Now we combine these terms:
$$-50 + 60i-40i - 48$$

Step3: Combine like terms

Combine the real parts and the imaginary parts separately.

• Real parts: $-50-48=-98$
• Imaginary parts: $60i - 40i = 20i$

Answer:

$-98 + 20i$