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# Geometry of Complex Roots

## Roots equally spaced around circles.

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Geometry of Complex Roots

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To graph the roots of a polynomial, first you must find one root. You only need one! Plot this root on the graph, draw a circle around the origin touching the root (now a point on your circle), and figure out how many degrees apart each root is using this formula:    .

The roots will be evenly spaced along the edge of this circle!

Remember: The number of roots is the power of the polynomial!

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1. What is the spacing in polar coordinates between the roots of the polynomial  ?
2. How many roots does  have?
3. Calculate the roots of  and represent them graphically.
4. How many roots does  have?
5. Calculate the roots of  and represent them graphically.
6. Describe how to represent the roots of  graphically without first solving the equation.