Aug 10, 2014 · $\begingroup$ Is $1+0i$ really the same as $1$ mathematically? $1+0i$ lies on a 2-dimensional complex plane while $1$ lies on a 1-dimensional line. $1+0i$ contains more mathematical information than $1$ so in my opinion they are not quite the same, but if you try to describe both of them together in either system, they would have the same value ...

Feb 7, 2015 · 0 + 0i has NO real part and NO imaginary part. That's not true: it has both a real part and an imaginary part, like every complex number. Its real part is 0, and its imaginary part is also 0. A real number is a complex number whose imaginary part is 0. The imaginary part of 0 + 0i is 0, and therefore it is a real number.

Oct 7, 2020 · @rschwieb "Imaginary zero" vs "complex zero" is 0i and 0+0i. The imaginaries are numbers in their own right. This represents a misapprehension about notation, I think. Writing "$0+0i$" is a little ambiguous.

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Here's a proof that I absolutely do not believe: take its complex conjugate, which is $\bigl({\bar i}\bigr)^{\bar i}=(1/i)^{-i}=i^i$.

Nov 9, 2014 · We know that, the real and imaginary axis meet at the origin which represents the complex number $0+0i$. As this point simultaneously lies on the real as well as the imaginary axis, we say that zero is both purely real and purely imaginary.

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May 2, 2017 · $\\mathbb Q$ is used to represent rational numbers. $\\mathbb R$ is used to represent real numbers. Is there an accepted symbol for imaginary numbers?

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Aug 6, 2015 · $\begingroup$ For complex exponent I agree with you that $0^0 = 1$ is not a good thing to have (not that it is impossible but just that it does not make anything better) for the reason in my answer.