Originally Posted by

**rcl333** I got confused on the operation and representation of complex numbers. It is

quite basic, and please help me understand. My question is as follows:

(1) Since 1=exp(2*pi*i), it seems that, for any real number a, we may have

exp(a*i)=exp((2*pi*i)*(a/(2*pi)))=(exp(2*pi*i))^(a/(2*pi))

= 1^(a/(2*pi))

=1

(2) For any complex number z, since 1+ exp(2*pi*i), it seems that

z^(1/4)=(1*z)^(1/4)=((exp(2*pi*i))^(1/4)*z^(1/4)

= (exp((pi/2)*i))*z^(1/4)

= i*z^(1/4)

by the same token, since 1=exp(-2*pi*i), it seems that

z*(1/4)=(-i)*z^(1/4)

All those are confusingly wrong, and I wish to understand why. Many thanks for you kindness to help.