So I want to graph: $$|z+1+i|<|z-2|$$
$z$ is a complex number.
After my calculation(with $z=x+iy$) I got: $$y<1-2x$$
When I put it in wolfram alpha the line is 1.5 on y axis and 0.8 on x axis. But the graph of function 1-2x is different. Why can’t I just graph the function and say that everything bellow it satisfies the inequality. What should I do to get the wolfram alpha graph or in other words the correct graph?
Your solution is not correct. In fact\begin{align}\require{cancel}\lvert x+yi+1+i\rvert<\lvert x+yi-2\rvert&\iff(x+1)^2+(y+1)^2<(x-2)^2+y^2\\&\iff\cancel{x^2}+2x+1+\cancel{y^2}+2y+1<\cancel{x^2}-4x+4+\cancel{y^2}\\&\iff6x+2y-2<0\\&\iff3x+y<1\\&\iff y<1-3x.\end{align}