Converting Complex Numbers Rectangular to Polar Here are the formal expression for converting rectangular to polar coordinates:  For the sake of this lesson, lets assume that the two forms of complex numbers are expressed this way:  Rectangular: a +jb
 Polar: cÐq
The objective is to express a +jb in in the form of cÐq. Recall how the same complex number can be represented two different ways: Citing a complex number with rectangular coordinates.  Citing the same complex number with polar coordinates.  Overlay the two coordinate system to show that there is a right triangle made up of all the important parts of the complex number. Converting from rectangular to polar coordinates is a matter of solving the triangle for the hypotenuse (c) and angle q. a = the length of the base of the triangle b = the height of the triangle c = the hypotenuse of the triangle q = the angle   From the Pythagorean theorem: That gives us the length component of the polar form in terms of the rectangular components, a and b. From basic trigonometry: That provides the angle component of the polar form, also in terms of the rectangular components. Converting from rectangular to polar coordinates for any complex number is a matter of solving those two equations. Example Convert 13.5 +j7.5 to polar form Step 1. Identify the components  a = 13.5
 b = 7.5
Step 2. Solve for the polar length Step 3. Solve for the polar angle: Step 4. Put it all together 13.5 +j7.5 = 15.4Ð29° Learn From More Examples  10 +j10 = 14.1Ð45°
 10 j10 = 14.1Ð45°
 1 + j3 = 3.16Ð71.6°
 2 + j20 = 20.1Ð84.3
 20 +j2 = 20.1Ð5.7°
 10 = 10Ð0°
 j10 = 10Ð90°
 3 +j5 = 5.8Ð59°
 5 +j2 = 5.4Ð21.8°
 3 j10 = 10.4Ð73.3°
