Why $0$ (zero) is a purely imaginary number?

Question

I was reading this Wikipedia article and found that $0$ is a purely imaginary number. Why? Is it because $i0=0$? So zero is the only number which is real as well as purely imaginary? Any explanations on this please?

Answer 1

It is just a matter of definitions.

Let $z$ be a complex number. Then, $z$ may be written (uniquely) as $z = a + bi$.

$a$ is said to be the real part of $z$.

$b$ is said to be the imaginary part of $z$.

$z$ is said to be a purely imaginary number if its real part is equal to $0$.

Hence, $0$ is a purely imaginary number because its real part is $0$.