Rectangular form is a representation in Cartesian coordinates, used both for complex numbers and for equations of curves.
The rectangular form of a complex number is
 |
where 
and 
are real numbers, 
is the real part, 
is the imaginary part, and
is the imaginary
unit. If 
is given in polar form with complex
modulus 
and complex argument 
, then 
and 
(Abramson 2021, §10.5).
For a plane curve, rectangular form means a Cartesian equation in 
and 
,
rather than parametric equations or a polar equation. For example, the unit
circle has rectangular form
 |
obtained from the parametric equations 
and 
by eliminating the parameter 
(Abramson 2021, §10.6). Restrictions
on a parameter must be retained as restrictions on
the resulting Cartesian equation when necessary
to describe the same curve.
