Calculate the derivative of a complex norm I'm stuck with a rather trivial looking question. How do you calculate the derivative of the norm of a complex number to it self? Like in

$$
\frac{d|a|^2}{da} = ?
$$

I think it would give rise to a real valued function but in stead I get 

$$
\frac{d|a|^2}{da} = \bar{a}
$$

I can't understand this result.

Thanks in advance.
Hint: For $z$ complex


  $$ |z|^2 =z\bar{z}. $$


Note:


  $$ z=x+iy \implies \bar{z}=x-iy .$$
For a complex variable a, |a|^2 derivative exist only at zero. Try evaluating at x_0+i*y_0 not zero. Approach from y=y_0 and you get 2*x_0 but approach from x=x_0 and you get -2*y_0*i. And at zero you get limit r^2 over re^(thetai) that go to zero.