If z=0 it's obvious. For all other complex numbers z=r*e^(θi), where r is a real number, and i=√-1.

Now, z= r*e^(θi)= r*(e^(2πi))^(θ/2π). Now as we know that e^(2πi)=1 we can write z =r*(1)^(θ/2π) → z=r.

What's wrong with this?

You get this even with numbers: (-1)^1 is/isn't the same as ((-1)^2)^(1/2)...

Posted by Federico Kereki on 2006-08-24 16:27:36