Question

help cauchy -riemann condition to check if its analytic??

Answer 1

the function is f(z)=sin z

Answer 2

Step I:
f(z)=sin(x+iy)
=sinxcoshy+icosxsinhy
u=sinxcoshy
v=cosxsinhy
partial derivative of u w.r.t x is
cosxcoshy
partial derivative of u w.r.t y is
sinxsinhy
partial derivative of v w.r.t x is
-sinxsinhy
partial derivative of v w.r.t y is
cosxcoshy
Step II:
partial derivative of u w.r.t x is=partial derivative of v w.r.t y
and
partial derivative of u w.r.t y is=(-partial derivative of v w.r.t x )
so it is analytic.

Answer 3

wow thanks

Answer 4

no problem