Problem

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

Solution

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 \(\boxed{6-\sqrt{23}i}\).

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