Does $f(x+yi):= \frac{xy}{x^2+y^2}$ have a continuous function in 0?

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Does $f(x+yi):= \frac{xy}{x^2+y^2}$ have a continuous function in 0 ?

I would start by changing it to $f(z) = \frac{xy}{|z|^2}$ but i cant find anything for xy

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Hint: What is the limit as $x \to 0$ along the line $y=0$? What about the line $y=x$?