Questions: Find the product and write the result in standard form. (6-3 i)(-2-8 i) (6-3 i)(-2-8 i) (Simplify your answer. Type your answer in the form a +b i.)

Transcript text: Find the product and write the result in standard form. \[ \begin{array}{l} (6-3 i)(-2-8 i) \\ (6-3 i)(-2-8 i)= \end{array} \] $\square$ (Simplify your answer. Type your answer in the form a $+b i$.)

Solution

Solution Steps

Step 1: Multiplication of Two Complex Numbers

To multiply two complex numbers $(a + bi)(c + di)$, we use the distributive property to expand the product: \[ (a + bi)(c + di) = ac + adi + bci + bdi^2 \] Since $i^2 = -1$, we simplify the expression to get $ac - bd + (ad + bc)i$. Substituting the given values, we get $6 \times -2 + 3 \times -8 + (6 \times -8 - 3 \times -2)i$.

Step 2: Simplification

After simplification, the real part is $-36$ and the imaginary part is $-42$.