*z*is real.

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?