Question

multiply (5 - 10i)(-3 + 8i) (1 point)

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first complex number by each term in the second complex number:
\((5 - 10i)(-3 + 8i)=5\times(-3)+5\times(8i)+(-10i)\times(-3)+(-10i)\times(8i)\)

Step2: Simplify each product

Calculate each term:
\(5\times(-3)= - 15\)
\(5\times(8i)=40i\)
\((-10i)\times(-3)=30i\)
\((-10i)\times(8i)=-80i^{2}\)
So the expression becomes \(-15 + 40i+30i-80i^{2}\)

Step3: Combine like terms and use \(i^{2}=-1\)

Combine the imaginary terms: \(40i + 30i=70i\)
Substitute \(i^{2}=-1\) into \(-80i^{2}\): \(-80\times(-1) = 80\)
Now combine the real terms: \(-15 + 80=65\)
So the expression is \(65 + 70i\)

Answer:

\(65 + 70i\)