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)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 hour ago

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: \[ \boxed{-56 + 58i} \]