Question

in your own words, explain what you know about a number that satisfies the equation $x^2=-1$.
type your response in the space below.

Explanation:

This number is not a real number, since squaring any real number gives a non-negative result. It is defined as the imaginary unit, denoted by $i$, which is the foundation of complex numbers (numbers of the form $a+bi$, where $a$ and $b$ are real numbers). $i$ follows rules like $i^2=-1$, $i^3=-i$, $i^4=1$, and it allows solving equations that have no real solutions.

Answer:

The number that satisfies $x^2=-1$ is the imaginary unit, called $i$. It is not a real number (since no real number squared is negative), and it is used to create complex numbers, which extend the real number system to solve equations that cannot be solved with only real numbers.