Look at this example
% -----initial curve---------
x=1:0.01:10;
y=sin(x);
plot(x,y,'r')
hold on
%---------rotated curve-----------------------
ang=20*pi/80 % rotation angle in rad
alpha=angle(x+i*y);
k=abs(x+i*y);
new_alpha=alpha+ang;
new_v=k.*exp(j*(new_alpha));
new_x=real(new_v);
new_y=imag(new_v);
plot(new_x,new_y)
