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.

See also

Cartesian Coordinates, Cartesian Equation, Complex Number, Exponential Form, Parametric Equations, Polar Form

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References

Abramson, J. "Polar Form of Complex Numbers" and "Parametric Equations." §§10.5-10.6 in Algebra and Trigonometry, 2nd ed. Houston, TX: OpenStax, 2021. https://openstax.org/books/algebra-and-trigonometry-2e/pages/10-5-polar-form-of-complex-numbers and https://openstax.org/books/algebra-and-trigonometry-2e/pages/10-6-parametric-equations.

Cite this as:

Weisstein, Eric W. "Rectangular Form." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RectangularForm.html

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