## Online Course Discussion Forum

### MC III-B Help

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.

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