Problem

Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. \[ -9-\sqrt{-37} \]

Solution

Step 1 :The given expression is \(-9-\sqrt{-37}\).

Step 2 :The expression contains a square root of a negative number, which is an imaginary number. The square root of -1 is represented by the imaginary unit $i$.

Step 3 :So, we can rewrite \(\sqrt{-37}\) as \(\sqrt{37}i\).

Step 4 :The expression then becomes \(-9 - \sqrt{37}i\).

Step 5 :Calculating the square root of 37 gives approximately 6.082762530298219.

Step 6 :So, the expression simplifies to \(-9 - 6.082762530298219i\).

Step 7 :Final Answer: The expression \(-9-\sqrt{-37}\) can be rewritten as a complex number as \(\boxed{-9 - 6.082762530298219i}\).

From Solvely APP
Source: https://solvelyapp.com/problems/jJV0rfkDbb/

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