Bit confused about a limit

I need to find this limit

$\displaystyle lim_{z\rightarrow{0}} \frac{Re(z)Im(z)}{|z|^2}$

Wolframalpha gives this limit as $\displaystyle 0$

Shouldn't this problem be equivalent

$\displaystyle lim_{(x,y)\rightarrow{(0,0)}} \frac{xy}{x^2+y^2}$

Wolframalpha gives this limit as non-existent

So now, I'm wondering, what makes these two formulations different?