Complex Variables

Find where in the complex plane the following function is analytic:

Question

Complex Variables

Find where in the complex plane the following function is analytic:

anonymous · Answer

$$\frac{ 1 }{ (y - ix + 1 + i + z)^4 }$$

i have the textbook's answer if needed but I don't understand why.

please explain ^_^

superdavesuper · Answer

Ur question is a lil unclear - which IS the function and what is the definition of 
"analytic"?  I assume z is the function....which is confusing as it could mean the z-axis in a 3-D coordinate system. Please clarify.

anonymous · Answer

it is a function f(z) where z is a function of x and y

superdavesuper · Answer

yup so z=f(x,y) I presume analytic means that the function is not infinity.  So the region is wherever on the complex plane except when z = -y + ix -1 -i because it will become 1/0.

anonymous · Answer

that isn't the textbook answer though..

amoodarya · Answer

did  z=x+iy ?

amoodarya · Answer

if yes 
put z=x+iy 
then simplify 
(x+y+1) +i(-x+1+y) =0+0i
so solve 
the system of equation 
you will find 
x=0 , y=-1
so your function is analytic always but not in z=-i

anonymous · Answer

yes z = x + iy

thank you very much ^_^

amoodarya · Answer

do you understand ?