I have to plot these:

1)$\displaystyle \mid z \mid= arg Z$

2)$\displaystyle log \mid z \mid= -2 arg Z$

For the first one I got sort of heart shaped graph. I have no idea where to find systematic approach to such kind of problems.

When i try to substitute l Z l= $\displaystyle \sqrt{x^2+y^2} $and $\displaystyle arg Z= \arctan{y/x}$ expressions get too complex...