Section+2.3+9-22


 * Section 2.3**

__Introduction__

Mrs. Tyson explained a question that arose on Wednesday: Why is it, when you make a triangle on a graph, why does the leg corresponding to the y value of the triangle not have i in it? For example, why is the magnitude of 3+4i, 5, instead of ?

Well, it's simple, = 1, so you would just be multiplying by 1, hence it's unneeded.

__Argumentation__

How do you find the argument of an angle?



Let's go back to geometry.. You could also use sine or cosine for this basic equation.

The argument of the complex number is the distance in radians (because degrees are bad) from the point (1,0) going around the circle, counter-clockwise to the hypotenuse of the triangle. The argument of the complex number in this picture (assuming c=1) is media type="custom" key="11856916". However if you go into any other quadrant, it may be a little different. Once you move into the 2nd quad. the argument of the complex number ismedia type="custom" key="11856616". With the third quadrant, it would be media type="custom" key="11856802". With the 4th quadrant, it would be media type="custom" key="11856738". This is always assuming one leg of the triangle is on the x axis.

__Polar Coordinates__

Usually, coordinates are given in the form (x,y). But sometimes it's useful to give them in the form of polar coordinates, such as when you're solving for the argument of a complex number. Polar coordinates take the form of (r,media type="custom" key="11880910"), where r is the hypotenuse of the triangle.

__Cis__

Cis refers to the following formula:media type="custom" key="11856680"or (in shorthand) media type="custom" key="11856710" where r is the hypotenuse of the triangle.