that complex numbers use a plane similar to the X and Y coordinate
system. In the complex system the X-axis is replaced by the
Real axis and the Y-axis by the imaginary (j) axis. The
imaginary axis is labeled "j" in the engineering world, while
mathematicians usually use "i". This yields a coordinate system as
Complex Number Conversion
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
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
converting from polar to rectangular for the equations used are:
A couple of
things to remember:
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
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,
3. Remember to account for metric
prefixes such as m, k etc.
Rectangular To Polar Conversion
converting from rectangular to polar for the equations used
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.
and 270 (-90 and
and 360 (0 and
This means you may need to add 180 degrees to determine the
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
enable it in your browser.