Analytic Function (3+x-iy)^7 in Domain [z]<2?

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(3+x-iy)^7 is analytic function of the complex variable z=x+iy in the domain [z]<2?
 
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Nope, [tex]f(z) = (3+x-iy)^7 = (3+\bar{z})^7[/tex]

[tex]\frac{df}{d\bar{z}} = 7(3+\bar{z})^6 \neq 0, \,\mathrm{for}\; |z| < 2.[/tex]