Question

The imaginary number i has the property that $i^2=\_\_\_$.

Short answer

The imaginary number i has the property $i^2=-1$.

Step-by-step solution

Step 1. Concept of complex number.

A complex number is of the form $a+bi$. Where a and b are some real numbers and i is the imaginary number.

The number a is known as the real part of the complex number and b is known as imaginary part of the complex number.

Step 2. Example for complex number.

In the complex number $3+5i$, the real part is 3 and the complex part is 5.

The imaginary number i is defined as the square root of negative one. That is, $i=\sqrt{-1}$.

Step 3. Evaluate the expression.

The imaginary number i is defined as the square root of negative unity. That is, $i=\sqrt{-1}$.

So, square both side of above expression to get

role="math" localid="1643989540962" $$\begin{gathered} {\left(i\right)}^2={\left(\sqrt{-1}\right)}^2 \\ {i}^2=-1 \end{gathered}$$

Thus, the imaginary number i has the property $i^2=-1$.