# Is zero imaginary or not? I think it is because 0=0i where i is iota. If it is imaginary then why every venn diagram of real and imaginary numbers on internet is disjoint. However, it should be overlapping.

Aug 29, 2017

Zero is a real number because it exists in the real plane, ie, the real number line. 8

#### Explanation:

Your definition of an imaginary number is incorrect.

An imaginary number is of the form $a i$ where $a \ne 0$

A complex number is of the form $a + b i$ where $a , b \in \mathbb{R}$. Therefore, all real numbers are also complex. Also, a number where $a = 0$ is said to be purely imaginary.

A real number, as stated above, is a number which has no imaginary parts. This means that the coefficient of $i$ is $0$.

Also, iota is an adjective meaning a small amount. We do not use it to denote the imaginary unit. Instead, $i$ stands for imaginary number, rather aptly.