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Re: MC III Help
by Dr. Kevin Wang - Saturday, July 16, 2022, 2:23 PM

2.30 talks about the area of a convex polygon whose vertices are the roots of the equation.  The equation has been written as a fourth power of a complex number equals another complex number.  So the four vertices actually form a square in the complex plane.  You need to figure out the area of the square.  So what matters is the length from the center to a vertex.  We can solve for the actual roots if we want to (there is a formula for that in the textbook).  But you can also figure out only the length.

2.32: you need to find out how to calculate the sum of the following type:

$$ X = 1 + 2r + 3r^2 + 4r^3 + \cdots + nr^{n-1} $$

Hint: Write out $rX$, and calculate $X - rX$, and see what you get.