Question

use the imaginary number i to rewrite the expression below as a complex number. simplify all radicals. -20 - √(-92)

Explanation:

Step1: Simplify the square root of a negative number

Recall that \(\sqrt{-a}=\sqrt{a}\cdot i\) for \(a>0\). So, \(\sqrt{-92}=\sqrt{92}\cdot i\).

Step2: Simplify \(\sqrt{92}\)

Factor 92: \(92 = 4\times23\). Then \(\sqrt{92}=\sqrt{4\times23}=\sqrt{4}\times\sqrt{23}=2\sqrt{23}\).

Step3: Substitute back into the original expression

The original expression is \(-20-\sqrt{-92}\). Substituting \(\sqrt{-92}=2\sqrt{23}i\) into it, we get \(-20 - 2\sqrt{23}i\).

Answer:

\(-20 - 2\sqrt{23}i\)