Question

1. solve the quadratic equations.

a. $x^2 = -16$

Explanation:

Step1: Recall imaginary unit

The imaginary unit \(i\) is defined as \(i = \sqrt{-1}\), so \(\sqrt{-a}=\sqrt{a}\cdot i\) for \(a>0\).

Step2: Solve for \(x\)

Given \(x^{2}=- 16\), take square roots on both sides: \(x=\pm\sqrt{-16}\).
Using the definition of \(i\), \(\sqrt{-16}=\sqrt{16}\cdot i = 4i\).
So \(x = \pm4i\).

Answer:

\(x = 4i\) or \(x=-4i\)