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Question

Conisder the complex valued funciton f(z)=2z3+b|z|3 where z is a complex variable. The value of b for which the function f(z) is analytic is


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Solution

The correct option is A 0

Let z=x+jy
f(z)=2(x+jy)2+b|(x+jy)|3
f(z)=2[x3+3x2jy3xy2jy3]+b(x2+y2)3/2
f(z)=2(x33xy2)+b(x2+y2)3/2+j[6x2y2y3]
Let f(z)=u+jv
u=2(x33xy2)+b(x2+y2)3/2
vy=6x26y2
Now f(z) to be analytic
ux=vy
and this is true only when,
b=0


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