\(5z^{2}\) = -500
First, divide both sides by 5. / Your problem should look like: \(z^{2} = -\frac{500}{5}\)
Second, simplify \(\frac{500}{5}\) to 100. / Your problem should look like: \(z^{2} = -100\)
Third, take the square root of both sides. / Your problem should look like: \(z = \sqrt{-100}\) , \(-\sqrt{-100}\)
Fourth, simplify \(\sqrt{-100}\) to \(( \sqrt{100i} )\) / Your problem should look like: z = ±\(\sqrt{100i}\)
Fifth, 10 × 10 = 100, so the square root of 100 is 10. / Your problem should look like: z = ±10i
Answer: z = ±10i OR z = 10i, -10i
