# Determine which of the following functions u are harmonic. For each harmonic function, find the conjugateharmonic function v and express u +iv as an analytic function of z.3.53.(b) 2xy + 3xy2-2y,(a) 3x2y + 2x2-уз-2y2,(d) e_2xy Sin(x2-y2).(c) xe-cosy-yez siny,

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z is a complex variable

z=x+iy

question attached in photo help_outlineImage TranscriptioncloseDetermine which of the following functions u are harmonic. For each harmonic function, find the conjugate harmonic function v and express u +iv as an analytic function of z. 3.53. (b) 2xy + 3xy2-2y, (a) 3x2y + 2x2-уз-2y2, (d) e_2xy Sin(x2-y2). (c) xe-cosy-yez siny, fullscreen
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Step 1

As per norms, the first three parts A, B and C are solved.To test if the given function is harmonic and find the harmonic conjugate in that case

Step 2

Basic definitions and Cauchy Riemann equations

Step 3

a) given function u is harmonic Remains ...

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