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Geometry of Complex Roots

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Practice Geometry of Complex Roots
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Geometry of Complex Roots

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:   $\frac{2\pi}{n}$ .

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 $x^6 = 12$ ?
2. How many roots does $x^{10}=1$ have?
3. Calculate the roots of $x^{10}=1$ and represent them graphically.
4. How many roots does $x^4=16$ have?
5. Calculate the roots of $x^4=16$ and represent them graphically.
6. Describe how to represent the roots of $x^6=1$ graphically without first solving the equation.