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### 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.
```
Associated Topics:
High School Imaginary/Complex Numbers

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