Tuesday, 27 January 2009

Complex Number Explained (2)

Complex number consists of real and imaginary terms to cover the concern that not all real number can satisfy any maths question.

An example was provided in this post (click the link for information).

What is then the different between this Real and Imaginary term?

In graphical form, the Real term is presented in the horizontal axis whereas the Imaginary term is along the vertical axis.

This is purposely so to has no impact of the Imaginary term on the Real term.
(Think in term of the cosine aspect of a pure Imaginary axis).
The overlapping portion of the Imaginary vertical part is ZERO on the Real axis.

See the diagram below for understanding.

The concept of this diagram is to allow learners visually see that the Real and Imaginary terms are unique in themselves and have no link to each other.

But another issue appears.

What is it?

Looking at the diagram, you will see that the complex number defined as Z = a + ib,
where "a" is the real term and "ib" is the imaginary,
will create directional value.

Some solution to specific maths problem requires the complete a + ib format.

Thus the introduction of complex number to offset the impossibility of solving equation using only real numbers, forces the angular dimension into the answer.

With this angular dimension coming into the mathematically picture, the principles of quadrant, as in the trigonometry studies, will be utilized to identify the various answers.

Complex number is then made "complex" mainly due to this directional information added to the normal Real numbers.

Do not be frighten off by this new addition, as, if you know very well how it comes about, you will welcome it. This imaginary term helps you solve many interesting maths equation that normal working cannot.

Love this complex number.


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