For the operations of multiplication, division, and exponentiation of complex numbers, it is generally much simpler to work with complex numbers expressed in polar form rather than rectangular form.
22.
The first is nice as an illustration of how some things are easy in polar form, and the last is general, but I wonder who benefits from the second equation.
23.
Where it is needed to add or subtract impedances, the cartesian form is more convenient; but when quantities are multiplied or divided, the calculation becomes simpler if the polar form is used.
24.
The polar form takes two samples from a different interval, [ " 1, + 1 ], and maps them to two normally distributed samples without the use of sine or cosine functions.
25.
Allen's Rule says that appendages like ears tend to be smaller in polar forms to minimize heat loss, and larger in tropical and desert equivalents to facilitate heat diffusion, and that the polar taxa are stockier overall.
26.
When one wants to solve the Dirichlet problem in a domain with rotational symmetry, the usual thing to do is to use the method of separation of variables for partial differential equations for Laplace's equation in polar form.
27.
In the same way as a complex number can be represented in a polar form, one has a " polar decomposition " for a complex measure : There exists a measurable function & theta; with real values such that
28.
To prove that the Engel curves of a function in Gorman polar form are linear, apply Roy's identity to the indirect utility function to get a Marshallian demand function for an individual ( i ) and a good ( n ):
29.
See for example this one I found on the first page with a google of'polar form'at where a science and engineering encyclopaedia encourages people to get it all wrong . talk ) 00 : 07, 11 October 2008 ( UTC)
30.
The mathematical formulation for a general conic section, with the other focus if any placed at a positive value ( for an ellipse ) or a negative value ( for a hyperbola ) on the horizontal axis, is then given in the polar form by
