Date: Wed, 24 Mar 1999 11:22:26 -0600 (CST)
Subject: complex numbers/polar coordinates
Who is asking: Student
|Complex numbers can be written in the form a+ib where a and b are real numbers. This gives rise to a graphical way to represent complex numbers in what is called the complex plane. Draw a coordinate system as you would for the Cartesian plane but label the horizontal axis the real axis and the vertical axis the imaginary axis. The complex number a+ib is then representated in the complex plane by the point with coordinates (a,b).|
If you introduce the polar coordinates notation into the Cartesian Plane as in the diagram then a/r = cos() and b/r = sin() so a = r cos() and b = r sin(). Hence the complex number a+ib can be written r cos() + i r sin() or more compactly r (cos() + i sin()).
You can see a use of this way of expressing complex numbers in the answer I gave to a teacher who asked about the square root of i.
I hope this helps
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