Evaluating complex numbers

1. Sep 12, 2004

Allday

How do you evaluate this expression algebraically.

$$e^{\sqrt{i}}$$

2. Sep 12, 2004

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).

3. Sep 12, 2004

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.

4. Sep 12, 2004

Allday

easy peasy. thanks

5. Sep 12, 2004

existence

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

6. Sep 13, 2004

Allday

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