ELT 115

Complex Number Conversion

A phasor quantity can be expressed in one of two forms, polar or rectangular. Polar notation refers to the phasor using its' magnitude (length) and angle (direction). Rectangular notation refers to the phasor using its' real component and imaginary component.

Consider the phasor below,

In the polar form the phasor would be expressed as having a magnitude of 5 units at an angle of 53 degrees. In the rectangular form the same phasor would be expressed as having 3 units in the positive real direction and 4 units in the positive imaginary (+j) direction.

Converting between polar and rectangular form is a technique that will be used very frequently when dealing with reactive circuit analysis and you must be equally comfortable converting from polar to rectangular and converting from rectangular to polar.

Polar To Rectangular
Conversion

When
converting from polar to rectangular for the equations used are:1. When entering theta use the value as measured from the positive real axis (0 degrees). The calculator will then give you the correct sign for the real and the imaginary components.

2. Be sure that your calculator is set to the angle units you are planning on using. If your problem is specified in degrees, make sure your calculator is set to degrees, not radians!

3. Remember to account for metric prefixes such as m, k etc.

Rectangular To Polar Conversion

When
converting from rectangular to polar for the equations used
are:The same reminders apply. Additionally you must be sure that you specify the angle correctly. Do not rely on the calculator to give you the correct angle. The calculator will try and specify an angle between 0 and 90 degrees.

If:

Real is: | and Imaginary is: | Angle must be between: |

Positive | Positive | 0 and 90 |

Negative | Positive | 90 and 180 |

Negative | Negative | 180 and 270 (-90 and -180) |

Positive | Negative | 270 and 360 (0 and -90) |

This means you may need to add 180 degrees to determine the angle correctly.

Practice, Practice,
Practice

The best way to become
proficient at anything is to practice! You can make up your
own problems, pick numbers for magnitude and angle the convert them to
real and imaginary components. Do the same converting the
other way. Pick values for real and imaginary components and convert to
magnitude and angle. You can check your results with the
pages below. The pages use javascript, so you may have to
enable it in your browser.

Check Rectangular to Polar | Check Polar to Rectangular |