I wanted to verify the answer to many questions on limits of complex numbers.
So, I tried using Wolfram Alpha for the same.
$$\lim_{z\to1}\frac{1-z^*}{1-z}$$ does not exist. [using path $y=m(1-x)$]
But, Wolfram Alpha computes the limit as $1$.
Am I wrong or Wolfram Alpha does not work for complex numbers?
Best Answer
You are right, since$$\lim_{t\to0,\,t\in\Bbb R}\frac{1-\left(\overline{t+1}\right)}{1-(t+1)}=1\quad\text{and}\quad\lim_{t\to0,\,t\in\Bbb R}\frac{1-\left(\overline{ti+1}\right)}{1-(ti+1)}=-1.$$