Real and Imaginary Numbers Confusion!<br> Are set of real numbers and set of imaginary numbers overlapping?<br> I think that they are overlapping because $0$ $0$ is both real and imaginary.

Question

If I am right then in the image below, I think imaginary numbers should be overlapping with real numbers.

Everywhere on the internet, venn diagram of real and imaginary number is disjoint not overlapping. Why?

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Answer 1 · 2017-08-29T21:20:53

No

An imaginary number is a complex number of the form $a + b i$ $a+bi$ with $b \neq 0$ $b != 0$

A purely imaginary number is a complex number $a + b i$ $a+bi$ with $a = 0$ $a = 0$ and $b \neq 0$ $b != 0$ .

Consequently, $0$ $0$ is not imaginary.