Question

solve for w.
2w² = -22
write your answer in simplified, rationalized form.
w = or w =

Explanation:

Step1: Divide both sides by 2

To isolate \( w^2 \), we divide both sides of the equation \( 2w^2 = -22 \) by 2. This gives us \( w^2=\frac{-22}{2}=- 11 \).

Step2: Take square root of both sides

We know that for a complex number, if \( x^2 = -a\) (where \(a>0\)), then \(x=\pm i\sqrt{a}\). Taking the square root of both sides of \(w^2=-11\), we get \(w = \pm\sqrt{- 11}\). Since \(\sqrt{-11}=\sqrt{11}\times\sqrt{-1}=i\sqrt{11}\), we have \(w = i\sqrt{11}\) or \(w=-i\sqrt{11}\).

Answer:

\(w = i\sqrt{11}\) or \(w=-i\sqrt{11}\)