Complex exponential function
With n = ln a a real number
u = az = enz= e n(x + i y ) = e nx∙
e iny
= e nx (cos (ny) +i sin(ny))
Expon. growth function n= |n| ➾ e z = e
nx (cos (ny) +i sin(ny))
Expon. damping function n = -|n| ➾ e -z=
e - nx (cos (ny) - i sin(ny))
The length of the vector z is expanded exponentially by the real
part of nz, its angle is rotated in the mathematical positive
sense by n times the imaginary part of z
n=1 leads to the familiar exponential growth function
u = e x (cos (y) +i sin(y))