Question

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.

Answer 1

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 `ai` where `a!=0`

A complex number is of the form `a+bi` where `a,b in RR`. 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.