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Equation of the Week #6: an introduction to math with Complex Numbers

Posted by DarthWho on May 15, 2011 at 12:00 AM

Complex numbers are not as difficult as they may first appear to be; this numeric system which is traditionally written in the form of:

A + B * i

Is the second of the division maths to be discovered; this is because like the real numbers the complex numbers are capable of being divided: however the complex numbers could also be written as

(A, B)

which brings us to a rather interesting point where it comes to these complex numbers: they form a twodimensional plane similar to the X,Y plane which is commonly used in programming.

now onto the basic mathematic operations:

Addition

(A + B * i) + (C + D * i) = (A + C) + (B + D) * i

Subtration

(A + B * i) - (C + D * i) = (A - C) + (B - D) * i

Multiplication: 

(A + B * i) * (C + D * i) = (A * C - B * D) + (A * D + B * C) * i

and Division:

(A + B * i)/(C + D * i) = ((A * C + B * D) + (B * C + A * D) * i)/(C ^ 2 + d ^ 2)


NEXT WEEK: the Complex Argument. (ARG(z))

Categories: Equation of the Week, Complex Numbers

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