Question
Simplify the expression shown below. \[ (3+\sqrt{-1})-(7+\sqrt{-25}) \]
Ask by Wilson French. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
-4 - 4i
\]
Solution
To simplify the expression:
\[
(3 + \sqrt{-1}) - (7 + \sqrt{-25})
\]
First, recognize that:
- \(\sqrt{-1} = i\)
- \(\sqrt{-25} = \sqrt{25 \times (-1)} = 5i\)
Substituting these values into the expression:
\[
(3 + i) - (7 + 5i)
\]
Now, distribute the subtraction:
\[
3 + i - 7 - 5i
\]
Combine like terms:
\[
(3 - 7) + (i - 5i) = -4 - 4i
\]
**Final simplified form:**
\[
-4 - 4i
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To simplify the expression \((3+\sqrt{-1})-(7+\sqrt{-25})\), we first need to simplify \(\sqrt{-25}\). Recall that \(\sqrt{-1} = i\) (the imaginary unit), so we can express \(\sqrt{-25}\) as: \[ \sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i \] Now, we can substitute \(\sqrt{-25}\) in the original expression: \[ (3+\sqrt{-1}) - (7+5i) \] This can be rewritten as: \[ (3 + i) - (7 + 5i) \] Now, we distribute the negative sign: \[ 3 + i - 7 - 5i \] Next, we combine the real and imaginary parts: \[ (3 - 7) + (i - 5i) = -4 - 4i \] Thus, the simplified expression is: \[ \boxed{-4 - 4i} \]
