Hi. I am supposed to sketch the set of points in the complex plane defined by
where <= is less than or equal to and I is the complex number.
By hand, we simply substitute z=x+I*y into the above inequality, expand and simplify to get
From here onwards, we sketch the straight line and shade the bottom region of the line.
In more challenging cases rather than getting a straight line, one has to complete the square to get an equation of a circle or ellipse. An example is |z-3| <= 2*|z+3| where one would substitute z=x+I*y to obtain 3x^2+30*x+3y^2+27 >=0 and then upon completing the square, we get (x+5)^2 + y^2 >= 16, giving a circle of centre (-5,0) and radius 4.
These obviously can be done by hand.
How would I do all these in Maple and plotting the line or circle or ellipse?