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+---
+title: Complex Number Plane
+---
+
+## Complex Numbers
+
+The complex number plane expresses a complex number in graphical form. The complex number is an extension of the real number
+line that adds an imaginary axis. This creates a two dimensional space with real and imaginary coordinates. 
+
+Complex numbers take the form (a + bi) with the real part being "a" expressed on the x-axis and "b" expressed on the y-axis. See the
+graph below.
+
+<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/af/Complex_number_illustration.svg/183px-Complex_number_illustration.svg.png" />
+
+A complex number that is on the x-axis is called purely real; while a complex number that is on the y-axis only is 
+called purely imaginary. The x-axis or real number line includes all real numbers. Therefore, the set of all real numbers is actually 
+a subset of the complex numbers. All real numbers, then are complex numbers who imaginary component is zero. 
+
+## Complex Polar Coordinates
+
+In polar form the cooordinates are the radius to the point in the complex plane and the angle from the x-axis. 
+
+The radius[r] is found from the pythagorean formula applied to the real and imaginary componenets. 
+
+r = sqrt(a^2 + b^2)
+
+The angle for the polar coordinate is found from taking the inverse tangent of the real and imaginary coordinates.
+
+@ = arctan(b/a) where x > 0
+@ = arctan(b/a) + pi where x < 0
+@ is undefined when x = 0
+
+<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/69/Complex_conjugate_picture.svg/300px-Complex_conjugate_picture.svg.png" />
+
+#### More Information
+-[Wikipedia:Complex number](https://en.wikipedia.org/wiki/Complex_number)
+-[Wolfram](http://mathworld.wolfram.com/ComplexNumber.html)