Question

2^i how to i simplify

Answer 1

2^i is a very weird number.
Just like saying that you have 3½ friends.... if you know what I mean, you are multiplying 2 "i" number of times, even though, "i" doesn't really have a value.

I can simplify i^2, but if it is 2^i, I would not be playing around with it.

Answer 2

\[i = \sqrt{-1}\]
\[2^{i} = 2^{\sqrt{-1}}\]
That's all I can come up with.

Answer 3

\[\Large 2^i=\left(e^{\ln2}\right)^i=e^{i\ln2}=\cos(\ln2)+i\sin(\ln2)\]

Answer 4

and that is to "simplify" ?

Answer 5

Well I would think a complex number in \(a+bi\) form is easier to work with, no?