I need help on another:
|z-4-i|+|z+4+i| > 1
Note that this can be written as |z - (4 + i)| + |z - (-4 - i)| = 1.
Now ..... if you're familiar with the locus definition of an ellipse then there's a very simple way of seeing that there's no solution to this equation.
Therefore the answer to the inequality is the entire complex plane ....
If you need an algebraic approach where you substitute z = x + iy etc. please say so.