# 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.