Arithmatic problem with Exponents: We know we know (-1)=e^i\pi=e^-i\pi, so...

[REDD]

Consider

(-1)^1/4=(-1)^1/4
we know (-1)=e^i\pi=e^-i\pi
so
(e^i\pi)^1/4=(e^-\pi)^1/4
(e^i\pi/4)=(e^-i\pi/4)
however
(e^i\pi/4)-(e^-i\pi/4) not equal to zero
So the above expression is not an equality.

Then whats wrong with it?

 

[mmm4444bot]

(e^i\pi)^1/4=(e^-\pi)^1/4

(e^i\pi/4)=(e^-i\pi/4)

How did you go from the first line above to the second?

The equation in red is false.

Your notation is not very good (eg: missing groupings symbols throughout). In the forum guidelines, there's a link to a page which explains how to type math expressions. Please check it out.

If you were trying to invoke LaTex, then you must enclose the code within delimiters. At this site, we use the tags \(\displaystyle \text{[te}\text{x]}\) and \(\displaystyle \text{[/te}\text{x]}\). Also, it's okay to simply type Pi. :cool:

 

[Dr.Peterson]

Consider

(-1)^1/4=(-1)^1/4
we know (-1)=e^i\pi=e^-i\pi
so
(e^i\pi)^1/4=(e^-\pi)^1/4
(e^i\pi/4)=(e^-i\pi/4)
however
(e^i\pi/4)-(e^-i\pi/4) not equal to zero
So the above expression is not an equality.

Then whats wrong with it?

The basic issue here is that any number has four fourth roots; you are picking a different one on each side.