Tuesday, 12 August 2008

Obtaining Angle Information From Complex Number

We all know that a complex number is written as Z = a + ib.

"a" is the REAL term, and "b" is the imaginary term.

If we are to plot these 2 terms on different axis on a diagram, we may get some information.
(This graph plotted is the Argand Daigram).

Plotting here means the Real term is on the horizontal axis and the Imaginary term on the vertical axis. We have to plot them on differeent axis as they are different in nature. One is Real number and the other is with sqrt(-1), imaginary item.

By plotting these 2 terms on a diagram (which is called the Argand Diagram), we will get a line with a specific length and an angle signifying its tilt from the horizontal axis.

How to extract the angle from the Argand diagram?

Using the trigonometric know-how, we can from the Trigonometric function of Tangent, extract the angle directly.

Example: 4 + i3

Real number = 4 (horizontal axis) and Imaginary number 3 (vertical axis)

Tan A = 3 / 4 ==> Angle A = tan -1 (3 / 4) = 36.870

Another example: 2 + i

Here the Real number is 2 and the Imaginary number is 1.

Tan B = 1 / 2 ===> Angle B = tan-1 (1/2) = 26.56 0.

A BONUS: How about "i"? ==> Answer is 90 degree upright (vertical) - no need to calculate.

Common mistake:
When the imaginary term is just "i" , the number is 1 and not ZERO ! The imaginary number value of 1 is "hidden" besides the "i".

So it is possible to find the angle of the line formed by a + ib through the use of the Trigonometric function Tangent.

The answer is a definite YES!
Nothing complex, right?


1 comment:

Anonymous said...

very useful.tnQ