Show this function obeys the Cauchy Riemann equations

**kiwijoey** · May 20th 2009, 07:55 PM

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.

**putnam120** · May 20th 2009, 08:35 PM

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

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