Question

ression to a + bi form: (7 + 7i)(-10 + 3i)

Explanation:

Step1: Use the distributive property (FOIL method)

Multiply each term in the first complex number by each term in the second complex number:
\((7 + 7i)(-10 + 3i)=7\times(-10)+7\times(3i)+7i\times(-10)+7i\times(3i)\)

Step2: Simplify each product

Calculate each product:
\(7\times(-10)= -70\)
\(7\times(3i)=21i\)
\(7i\times(-10)= -70i\)
\(7i\times(3i)=21i^{2}\)
Recall that \(i^{2}=-1\), so \(21i^{2}=21\times(-1)= -21\)

Step3: Combine like terms

Combine the real parts and the imaginary parts:
Real parts: \(-70 - 21=-91\)
Imaginary parts: \(21i-70i = -49i\)

Answer:

\(-91 - 49i\)