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Evaluating complex numbers

  1. Sep 12, 2004 #1
    How do you evaluate this expression algebraically.

    [tex]
    e^{\sqrt{i}}
    [/tex]
     
  2. jcsd
  3. Sep 12, 2004 #2

    robphy

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    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).
     
  4. Sep 12, 2004 #3

    Tide

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    If you take [itex]i = e^{i \frac {pi}{2}}[/itex] then [itex]\sqrt i = e^{i \frac {pi}{4}}[/itex]. Just write it in trig form and put into your expression.
     
  5. Sep 12, 2004 #4
    easy peasy. thanks
     
  6. Sep 12, 2004 #5
    Not quite. Don't forget the second root exp[i(pi/4 + pi)].
     
  7. Sep 13, 2004 #6
    Ahh yes, those pesky multiple values. That complex plane will eventually bend to my will.
     
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