Complex Numbers: 0^i

Date: 11/26/2002 at 01:51:28
From: Tim H
Subject: Complex Numbers

What does 0^i equal?

Date: 11/26/2002 at 11:18:01
From: Doctor Ian
Subject: Re: Complex Numbers

Hi Tim,

Good question! I don't believe anyone has asked us this before, which
is somewhat surprising. 

In any case, note that 

  0^i = e^(ln(0^i))

      = e^(i*ln(0))

      = cos(ln(0)) + i*sin(ln(0))

Since ln(0) is undefined, the quantity 0^i is also undefined.

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 11/27/2002 at 01:02:30
From: Tim H
Subject: Thank you (Complex Numbers)

Thank you for answering my question.