Question

What is $i^{2}$?

Answer 1

In order to do this question, first you need to know what i is. i is an imaginary number. The square root of -1 that is $\sqrt{-1}$ is represented by i. It is also sometimes represented as j. i is a very important number in mathematics. It is used in various topics. In the question we should find $i^{2}$. Therefore, the square root of -1 is -1. Hence, you can find the answer.

Complete step by step solution:
Here is the step wise solution.
The first part is to know what i is. i is an imaginary number. An imaginary number is a number which is the square root of a negative number. Normally, we know that the square root of a negative number does not exist. Therefore, it is called an imaginary number.
i is a very important imaginary number. i is the square root of -1. That is
$i = \sqrt{-1}$
Therefore, to find the square of i that is $i^{2}$, we should just square the above equation. Therefore, we get the answer for $i^{2}$ as:
$\Rightarrow i^{2} = \left(\sqrt{-1}\right)^{2}$
$\Rightarrow i^{2} = -1$
Therefore, we get the final answer of the question, what is $i^{2}$ as -1.

Note: You need to know what the number i means if you have to solve the question. Without this knowledge, you will not be able to solve the question. i is very important in mathematics as well as physics. It is used in complex numbers, quadratic equations, electricity, control systems and many more. In physics, the imaginary numbers are usually represented with j.