Question
Simplify
(-8-3i)(5+i)
write your answer in the form a + bi
(-8-3i)(5+i)
write your answer in the form a + bi
Answers
GPT-4o mini
To simplify \((-8 - 3i)(5 + i)\), we can use the distributive property (also known as the FOIL method for binomials).
Let's calculate it step by step:
\[
(-8)(5) + (-8)(i) + (-3i)(5) + (-3i)(i)
\]
Now, we perform each multiplication:
1. \((-8)(5) = -40\)
2. \((-8)(i) = -8i\)
3. \((-3i)(5) = -15i\)
4. \((-3i)(i) = -3i^2\)
Remember that \(i^2 = -1\), so we have \(-3i^2 = -3(-1) = 3\).
Now, we combine all the terms together:
\[
-40 - 8i - 15i + 3
\]
Combine the real parts and the imaginary parts:
Real part: \(-40 + 3 = -37\)
Imaginary part: \(-8i - 15i = -23i\)
Putting it all together, we get:
\[
-37 - 23i
\]
Thus, the simplified form of \((-8 - 3i)(5 + i)\) is:
\[
\boxed{-37 - 23i}
\]
Let's calculate it step by step:
\[
(-8)(5) + (-8)(i) + (-3i)(5) + (-3i)(i)
\]
Now, we perform each multiplication:
1. \((-8)(5) = -40\)
2. \((-8)(i) = -8i\)
3. \((-3i)(5) = -15i\)
4. \((-3i)(i) = -3i^2\)
Remember that \(i^2 = -1\), so we have \(-3i^2 = -3(-1) = 3\).
Now, we combine all the terms together:
\[
-40 - 8i - 15i + 3
\]
Combine the real parts and the imaginary parts:
Real part: \(-40 + 3 = -37\)
Imaginary part: \(-8i - 15i = -23i\)
Putting it all together, we get:
\[
-37 - 23i
\]
Thus, the simplified form of \((-8 - 3i)(5 + i)\) is:
\[
\boxed{-37 - 23i}
\]