evaluating complex numbers

[Allday]

How do you evaluate this expression algebraically.


e^{\sqrt{i}}

[robphy]

Since i=exp(i*pi/2), you can determine easily sqrt(i) in polar form, then in rectangular form: a+bi. Then you can evaluate exp(a+bi).

[Tide]

If you take i = e^{i \frac {pi}{2}} then \sqrt i = e^{i \frac {pi}{4}}. Just write it in trig form and put into your expression.

[Allday]

easy peasy. thanks

[existence]

Not quite. Don't forget the second root exp[i(pi/4 + pi)].

[Allday]

Ahh yes, those pesky multiple values. That complex plane will eventually bend to my will.