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Yes \(z = a+ib\)
then \(|z| = \sqrt{a^2+b^2}\)

oh my O_O! so a and b is connected to z then

let me know if tht above is like really really wrong or whatever

|dw:1436697803754:dw|

\(f'(3+i2)\) in each direction need not be same, so the derivative doesn't exist

Wow! how did you get that
wil try to figure it out... have good sleep :)

\[\frac{d \mid z \mid}{dz} = \cos(\theta) +isin(\theta), z =(r, \theta) \]

\[\large \frac{d|z|}{dz} = e^{i\arg(z)}\]
?
this looks interesting

http://mathworld.wolfram.com/AbsoluteValue.html

if you know anyways (I know you are the wolfram master)

oh

As expected it says there are no solutions

I completely misread that

\[\dfrac{d|z|}{dz} \Bigg|_{\text{over circle}} = 0\]
?

?? what does that over circle mean??

integration?

http://www.wolframalpha.com/input/?i=limit%28%28%7Cz%2Bh%7C-%7Cz%7C%29%2Fh%2Ch%3D0%29

oh but I think h there is meaning change in real number only

i have i more reason which proves that u can't do differentiation with complex numbers

yes

@ganeshie8 have you ever head of something called cauchy riemann equation?

heard*

since you know z is complex

Holomorphic Function?

i think you are right