Let's "prove" that every complex number z
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?
(In reply to I think this is wrong because...
in the very first step....
when we are raising e^iè to (2ð/2ð), it means that we r first raising it to 2ð and then taking its (2ð)th root. but taking an irrational root of a number is invalid!
Posted by vivek
on 2006-09-22 14:15:10