The multivalued cube root function
Place the cursor over the image to start the animation.
Place the cursor over the image to start the animation.
Place the cursor over the image to start the animation.
Place the cursor over the image to start the animation.
Click on the image to get a pdf file.
The above image is a modified picture that I found at the Wikipedia page about the unit circle. If you compare the picture on the Wikipedia page you will notice that I labeled the angles with the values of the principal argument, that is the values from the interval . I also removed the degree values, since degrees are not used in complex analysis.
Here is the Wikipedia article about: (Euler's formula). Please read the whole article, or read the parts that you find interesting. The proof that I presented in class is one of three proofs presented at the bottom of the page.
For arbitrary complex numbers $z$ and $w$ we have: .