# Complex Analysis/Complex differentiability and the Cauchy‒Riemann equations

If sin(x+iy)=p+iq ,then find p and q.

Sol. Here

￼sin(x+iy)=p+iq

=> sinx.cos(iy)+cosx.sin(iy)=p+iq

=>sinx.coshy+icosx.sinhy=p+iq

[sin ix= sinhx, cos ix= coshx]

On comparing both the sides, we get

=> p=sinx.coshx and q= Complex Analysis^{[1]}

- ↑ If sin(x+iy)=p+iq ,then find p and q.