I have a pretty basic question about complex numbers.
Let $z=x+yi$ be a complex number, I want to compute the real and imaginary parts of the number $w=e^{e^z}$.
Thanks in advance for any help.
I have a pretty basic question about complex numbers.
Let $z=x+yi$ be a complex number, I want to compute the real and imaginary parts of the number $w=e^{e^z}$.
Thanks in advance for any help.
As DJC and Fredrik Meyer suggest, you need a repeated application of
$e^z=e^{x+iy}=e^x(\cos y+i\sin y)= e^x\cos y+ie^x\sin y$
to get something like
$e^{e^z}=e^{e^x\cos y}\cos (e^x\sin y)+ie^{e^x\cos y}\sin (e^x\sin y).$