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Originally Posted by AntonioLao when the real argument is zero, the complex number becomes pure imaginary. When the imaginary argument is zero, the complex number becomes pure real.
These are respectively found the imaginary axis and real axis. |
True, I know. But they do count in the set of all complex numbers.
About Euler's identity, e^ipi is a real number, -1. This means that some combinations of reals and imaginaries can give still realsor imaginaries, not complex numnbers, even when no part of the number is zero.