The cosh() function does not accept the complex number as the argument.
https://www.originlab.com/doc/OriginC/ref/cosh
The workaround is to use cos() function since cosh(x) = cos(ix).
complex cc = cos(1i*(1+1i*tau*alpha*omega));
y1 = cc.m_re;
y2 = cc.m_im;
James