Polar form, MATLAB in Mathematics

Polar Form:

Any complex number z = a + bi can be thought of as a point (a,b) or vector in the complex plane in which the horizontal axis is the real part of z, and the vertical axis is an imaginary part of z. Therefore, a and b are the Cartesian or rectangular coordinates. As a vector can be presented by either it's rectangular or polar coordinates, a complex number can be given also by its polar coordinates r and θ, here r is the magnitude of the vector and θ is an angle.

To convert from the polar coordinates into the rectangular coordinates:

a = r cos θ

b = r sin θ

To convert from the rectangular into polar coordinates:

1607_polor form.png

Therefore, a complex number z = a + bi can be written as r cos θ + (r sin θ )i, or z = r (cos θ  + i sin θ )

As ei θ = cos θ + i sin θ , a complex number can also be written as z = rei θ. In MATLAB, r can be found by using the abs function, and there is a special built-in function to find θ, known as angle.

>> z1 = 3 + 4i;

r = abs(z1)

r =

   5

>> theta = angle(z1)

theta =

   0.9273

>> r*exp(i*theta)

ans =

   3.0000 + 4.0000i

Posted Date: 10/22/2012 8:56:23 AM | Location : United States







Related Discussions:- Polar form, Assignment Help, Ask Question on Polar form, Get Answer, Expert's Help, Polar form Discussions

Write discussion on Polar form
Your posts are moderated
Related Questions
Writing variables to a File: The save command is used to write variables to a file, or to append the variables to a MAT-file. By the default, save function writes to a MAT-fil

Fliplr function: The fliplr function "flips" the matrix from left to right (in another words the left-most column, the first column, become the last column and so on), and the

Pie chart - plot functions: The MATLAB also has a function pie which will generate a pie chart. Calling the function with the form pie (vec) draws a pie chart, by using the pe

Write a MATLAB function [d1, u1, l1, c1, r1] = NaiveGaussArrow(d, u, l, c, r) that takes as input the 5 vectors de ned above representing A. This function performs Naive Gauss redu

bar and barh functions: For a matrix, the bar and barh functions will group altogether the values in each and every row. The illustration is as shown: rm = randint(2,4,[1

strvcat function - concatenation: The function strvcat will concatenate it vertically, that means that it will generate a column vector of the strings.   >> strvcat(fir

Polar Form: Any complex number z = a + bi can be thought of as a point (a,b) or vector in the complex plane in which the horizontal axis is the real part of z, and the vertica

Sorting The Sorting is a process of putting a list in order; either in descending (maximum to minimum), or ascending (minimum to maximum) order. For illustration, here is a li

Creating Customized strings: There are many built-in functions which create customized strings, including blanks, char, and sprintf. We know that the char function can be u

Strings as Vectors: The Strings are considered as vectors of characters-or in another words, a vector in which each and every element is a single character-so numerous vector