Complex Analysis/Complex differentiability and the Cauchy‒Riemann equations

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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]

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