Question
\[ (8+3 i)+(-7+i) \] Write your answer in the form \( \mathrm{a}+\mathrm{b} i \).
Ask by Tucker Cox. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The sum is \(1 + 4i\).
Solution
To add the complex numbers \((8 + 3i)\) and \((-7 + i)\), follow these steps:
1. **Add the real parts:**
\[
8 + (-7) = 1
\]
2. **Add the imaginary parts:**
\[
3i + i = 4i
\]
3. **Combine the results:**
\[
1 + 4i
\]
So, the sum is \(1 + 4i\).
\(\boxed{1 + 4i}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve the expression \( (8 + 3i) + (-7 + i) \), we can combine the real parts and the imaginary parts separately. The real parts are: \[ 8 + (-7) = 8 - 7 = 1. \] The imaginary parts are: \[ 3i + i = 3i + 1i = 4i. \] Putting it all together, we get: \[ 1 + 4i. \] So, the final answer in the form \( a + bi \) is \( 1 + 4i \).
