Complex operator $i$ and Exponents I am trying to understand the complex numbers and exponents.
I came across this question. I wonder how to explain the difference between $${2\cdot i} \text{ and } 2^i$$ as $i=\sqrt{-1}$
edit:
Rather than explaining the meaning of above two numbers in yet another equally difficult mathematical form.. i am more interested in knowing as to in which situation do we need to use one of the above numbers and in which other situation we would use the other number.
From many of the answers I now understand that bot of the above numbers are complex numbers but they are of different types in a way that one has a single value while the other has more than 1 values. So in which practical situation do we prefer to use one form and in which the other?

$$2^i=\mathrm e^{i\ln 2}=\cos(\ln 2)+i\sin(\ln 2)\ne 2i. $$
