Question
Express \( \sqrt{-25} \) as a complex number (in terms of \( i \) ): \( \sqrt{-25}=\square \)
Ask by Gordon Olson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \sqrt{-25} = 5i \)
Solution
Calculate or simplify the expression \( \sqrt{-25} \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{-25}\)
- step1: Evaluate the power:
\(\sqrt{25}\times \sqrt{-1}\)
- step2: Evaluate the power:
\(\sqrt{25}\times i\)
- step3: Evaluate the power:
\(5i\)
The complex number representation of \( \sqrt{-25} \) is \( 5i \).
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Mind Expander
To express \( \sqrt{-25} \) as a complex number, we start by recognizing that the square root of a negative number involves the imaginary unit \( i \), where \( i = \sqrt{-1} \). Therefore, we can rewrite \( \sqrt{-25} \) as follows: \[ \sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i \] Thus, the expression in terms of \( i \) is: \[ \sqrt{-25} = 5i \]