The word that the ImplicitPlane object uses for the type of answer that is expected depends on the number of variables in the context. If it is two variables, it is called an implicit line, and if three or more, an implicit plane. Note that it is not the number of variables in the equation, since in (
x,
y,
z)-space, you would still want
x+y=1 and
y=3 to be referred to as planes, not lines or points.
In your case, you have variables x and y, and then add z and i. That makes for four variables, so it is called a plane.
There are a couple of ways around this. Firs, since your z and i are only used to display the original equation, you could use a separate context for that (the Complex context, so you don't have to add the variables). For example,
Context("ImplicitPlane");
Context()->variables->are(x=>"Real",y=>"Real");
$x1 = non_zero_random( -3, 3, 1 );
$y1 = non_zero_random( -3, 3, 1 );
$r1 = 1; #RHS of the complex equation
$soln1 = ImplicitPlane("2*$y1*y=(-2*$x1)*x + $x1*$x1 + $y1*$y1 ");
Context("Complex");
$f1 = Compute("abs((z - $x1 - $y1 i)/z)")->reduce->TeX;
On the other hand, this will mean that if the student enters z or i in the answer, she will get an error message about unknown variables. If you want to have z and i be known in the answer blank, then a solution is to create the ImplicitPlane object first before adding the variables to the context. The name is determined at the time the object is created, so if there are only two at that point, it will be called a line.
Context("ImplicitPlane");
Context()->variables->are(x=>"Real",y=>"Real");
$x1 = non_zero_random( -3, 3, 1 );
$y1 = non_zero_random( -3, 3, 1 );
$r1 = 1; #RHS of the complex equation
$soln1 = ImplicitPlane("2*$y1*y=(-2*$x1)*x + $x1*$x1 + $y1*$y1 ");
Context()->variables->add(z=>'Complex');
Context()->constants->redefine(i=>{from=>"Complex"});
$f1 = Compute("abs((z - $x1 - $y1 i)/z)")->reduce->TeX;
Another possibility is simply to set the name used for the object yourself:
ANS($soln1->cmp(cmp_class=>"an Implicit Line"));
or
$soln1 = ImplicitPlane("2*$y1*y=(-2*$x1)*x + $x1*$x1 + $y1*$y1 ")->with(implicit=>"line");
to set the type on the object itself.
Hope one of these does the trick.