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?
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1$\begingroup$ 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 $\endgroup$– happymathNov 26, 2015 at 6:22
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4$\begingroup$ Or maybe because $0$ is the only intersecting point of real and imaginary axes. $\endgroup$– Kushal BhuyanNov 26, 2015 at 6:23
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$\begingroup$ 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. $\endgroup$– user65203Nov 28, 2015 at 14:11
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1 Answer
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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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7$\begingroup$ At the same time, it can also be said purely real, real, imaginary or complex (!). $\endgroup$– user65203Nov 28, 2015 at 14:16