Igebra $2> 1.1$ Introduction to complex numbers $5 \mathrm{~W}$
You ha
Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals.
\[
6-\sqrt{-23}
\]
i
Submit
Answer
So, the simplest form of the complex number is \(\boxed{6-\sqrt{23}i}\).
Step 1 ：Given the expression is \(6-\sqrt{-23}\).
Step 2 ：The square root of a negative number is an imaginary number. So, we can rewrite \(\sqrt{-23}\) as \(\sqrt{23} \cdot \sqrt{-1}\).
Step 3 ：We know that \(\sqrt{-1}\) is represented by the imaginary unit \(i\).
Step 4 ：So, \(\sqrt{-23}\) can be rewritten as \(\sqrt{23}i\).
Step 5 ：Therefore, the expression \(6-\sqrt{-23}\) can be rewritten as a complex number \(6-\sqrt{23}i\).
Step 6 ：So, the simplest form of the complex number is \(\boxed{6-\sqrt{23}i}\).
