For this the contributions from each point must be added as a sum of complex numbers where each complex number ( in polar form ) represents the received intensity like the scalar case but with the added fact that the distance from the source gives an angular phase delay.
32.
In the section of this article " General polar form ", the equaitons are given for expressing the polar form of the equation for an ellipse if we know a few parameters like the semi major and semi minor axes etc . To this end, the equation is given defining Q ( theta ).
33.
In the section of this article " General polar form ", the equaitons are given for expressing the polar form of the equation for an ellipse if we know a few parameters like the semi major and semi minor axes etc . To this end, the equation is given defining Q ( theta ).
34.
If the quadratic equation ax ^ 2 + bx + c = 0 with real coefficients has two complex roots & mdash; the case where b ^ 2-4ac requiring " a " and " c " to have the same sign as each other & mdash; then the solutions for the roots can be expressed in polar form as
35.
Intuitive, when you pass a signal through a filter, it may attenuate some frequencies in different degrees ( Multiply them ), but it also may rotate the phase of the frequencies, and complex numbers define this multiplication for both components of each frequency ( Either expressed as sine waves in quadrature or the magnitude and phase of a single one, AKA rectangular and polar form ) while real numbers by themselves only explain intuitively the magnitudes.
