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**Dgphru** Hi, can someone please help me..

Question: Write the function $\displaystyle f(z) = sin2(z) $in the form $\displaystyle f = u + iv $, with u and v real functions. Hence show that f(z) is an entire function.

here's my working:

$\displaystyle

f(z) = sin2(z), where z = x + iy$

$\displaystyle = sin2(x + iy)

= sin 2x cos 2iy + cos 2x sin iy $

since,

$\displaystyle f(z) = u + iv $

thus $\displaystyle u(x,y) = 0, v (x,y) = sin 2x cos 2iy + cos 2x sin iy $

then i do partial derivaties to satisfy cauchy riemann equations..

partial of u wrt x = 0

partial of v wrt y = cos 2x i sin iy - 2i sin 2x cos 2iy

partial of u wrt y = 0

partial of v wrt x = ..

well i know i did it wrong coz

partial of u wrt x = partial of v wrt y

and

partial of u wrt y = - partial of v wrt x

so can someone please help me??