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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?

Najib Idrissi
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Kushal Bhuyan
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    I think any number with no real part is called a purely imaginary number So here since the real part is zero then it is purely imaginary – happymath Nov 26 '15 at 06:22
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    Or maybe because $0$ is the only intersecting point of real and imaginary axes. – Kushal Bhuyan Nov 26 '15 at 06:23
  • The referenced link is slightly self-contradicting as it first says "... are all purely imaginary or zero", then "... zero is also considered purely imaginary". The second expression is better. –  Nov 28 '15 at 14:11

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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 $0$.

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    At the same time, it can also be said purely real, real, imaginary or complex (!). –  Nov 28 '15 at 14:16