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> Evaluate $\lim\_{z\to 0}\frac{\bar z}{z}$ where $z=x+iy$
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My try:

$$\lim\_{z\to 0}\frac{\bar z}{z}=\lim\_{z\to 0}\frac{x-iy}{x+iy}$$

$$=\lim\_{z\to 0}\frac{(x-iy)(x-iy)}{(x+iy)(x-iy)}$$

$$=\lim\_{z\to 0}\frac{x^2-y^2-2ixy}{x^2+y^2}$$

$$=\lim\_{z\to 0}\frac{x^2-y^2}{x^2+y^2}-\frac{2ixy}{x^2+y^2}$$

I can't solve it from here. My teacher says that the limit doesn't exist but I don't know how & why. Please help me solve this question