I am unable to spot the error in this calculation...!! What's wrong here...??



Thanks and regards,
Rahul

 

hi,
Check out this video.
E

 

The mistake is here

 

The mistake is here
View attachment 223647

So what is the mistake?

Is it that (a^x)^2 isn't a^(2x)? Or is it that (-1)^2 isn't 1?

If you are being careful, it should be noted that

\(e^{ix} \; = \; e^{i\left(x+2n\pi\right)}\)

I would say that the problem is here:

\(ln \left( e^{2 \pi i} \right) \; = \; 2 \pi i\)

This should be

\(ln \left( e^{2 \pi i} \right) \; = ln \left( e^{2n \pi i} \right) \; = \; 2n \pi i \;\; \text{(n is an integer)}\)

So now in the next set you have

\(2n \pi i \; = \; 0 \)

which is true if we choose n=0

 

solve for (e^(i pi))^2

the issue is you're using complex "i"

 

Would it help to use Euler's identity?