Question
Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \[ \sqrt{-1} \]
Ask by Pierce Young. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
i
\]
Solution
To rewrite the expression \(\sqrt{-1}\) using the imaginary number \(i\), we use the fundamental definition of \(i\):
\[
i = \sqrt{-1}
\]
So, the expression \(\sqrt{-1}\) can be directly written as:
\[
i
\]
This is already in the standard form of a complex number \(a + bi\), where \(a = 0\) and \(b = 1\). Therefore, the simplified complex number is:
\[
0 + i \quad \text{or simply} \quad i
\]
**Final Answer:**
\[
i
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
The expression \( \sqrt{-1} \) can be expressed as the imaginary unit \( i \). In the realm of complex numbers, \( i \) is defined such that \( i^2 = -1 \). Therefore, when you simplify \( \sqrt{-1} \), you simply get \( i \). In complex number terms, every complex number can be represented as \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part. In this case, since \( \sqrt{-1} \) simplifies to \( i \), you could say your complex number is \( 0 + 1i \) or just \( i \).
