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Is zero purely imaginary?
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Zero is not purely imaginary.
Pros
Cons
Purely imaginary numbers are a subset of the complex numbers with a non-zero imaginary component.
The purely real and purely imaginary numbers are disjoint sets.
The reciprocal of any purely imaginary number is well defined.
The condition that a complex number is purely imaginary is equivalent to the statement that z*=-z, where * represents the complex conjugate.
The standard definition of the purely imaginary numbers are all real numbers multiplied by i. Since 0i=0, and 0 is a real number, 0 is both real and purely imaginary.
If the purely imaginary numbers are defined as all complex numbers such that z^2=-z, then 0 must be purely imaginary.
The purely imaginary numbers are not a group under addition.
The purely imaginary numbers are no longer continuous.
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