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i Power Seen through with ln()

Date: 11/25/2010 at 05:22:55
From: AMAN
Subject: COMPLEX NUMBER

What is the value of 1 raised to the power square root of (-1)?



Date: 11/25/2010 at 06:40:03
From: Doctor Ali
Subject: Re: COMPLEX NUMBER

Hi Aman!

Thanks for writing to Dr. Math.

You can begin like this:

    A = 1^i

Now take the natural logarithm of both sides:

    ln(A) = i * ln(1)

Therefore,

    A = e^(i * ln(1))

We know that

    ln(1) = 0

So,

    A = e^(i * 0) = ...

Does that make sense?

- Doctor Ali, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Imaginary/Complex Numbers
High School Logs

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