Question

Simplify the expression to a + bi form:
left parenthesis, minus, 1, plus, 8, i, right parenthesis, left parenthesis, 8, plus, 6, i, right parenthesis
(−1+8i)(8+6i)

Answer 1

To simplify the expression \((−1 + 8i)(8 + 6i)\), we'll use the distributive property (also known as the FOIL method for binomials).

Let's calculate it step by step:

1. **First**: Multiply the first terms:
\[
-1 \cdot 8 = -8
\]

2. **Outer**: Multiply the outer terms:
\[
-1 \cdot 6i = -6i
\]

3. **Inner**: Multiply the inner terms:
\[
8i \cdot 8 = 64i
\]

4. **Last**: Multiply the last terms:
\[
8i \cdot 6i = 48i^2
\]

Since \(i^2 = -1\), we can replace \(48i^2\) with \(-48\):
\[
48i^2 = 48(-1) = -48
\]

Now, combining all these results:
\[
-8 - 6i + 64i - 48
\]

Combine the real parts:
\[
-8 - 48 = -56
\]

Combine the imaginary parts:
\[
-6i + 64i = 58i
\]

So the simplified expression is:
\[
-56 + 58i
\]

Thus, the answer in \(a + bi\) form is:
\[
\boxed{-56 + 58i}
\]