Can a set containing $0$ be purely imaginary?

A complex number is said to be purely imaginary if it's real part is zero. Zero is purely imaginary, as it's real part is zero.


0 is both purely real and purely imaginary. The given set is purely imaginary. That's not a contradiction since "purely real" and "purely imaginary" are not fully incompatible. Somewhat similarly baffling is that "all members of X are even integers" and "all members of X are odd integers" is not a contradiction. It just means that X is an empty set.

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Complex Numbers

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