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:
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First: Multiply the first terms: \[ -1 \cdot 8 = -8 \]
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Outer: Multiply the outer terms: \[ -1 \cdot 6i = -6i \]
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Inner: Multiply the inner terms: \[ 8i \cdot 8 = 64i \]
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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: \[ \boxed{-56 + 58i} \]