Thread: Show this function obeys the Cauchy Riemann equations

f(z) = sin(2z). I have so far got to:

f(x + iy) = sin[2(x+iy)
f(x + iy) = sin(2x) cos(2iy) + cos(2x) sin(2iy).

I'm stuck on converting this into the form f(x + iy) = u(x,y) + iv(x,y).

Any help on that step? After that step I should be ok.

I haven't tried to work it all out but I would suggest that you write $\displaystyle \sin(x)=\frac{e^{ix}-e^{-ix}}{2i}$.