Need help with Density of random variable.

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Homework Statement



position of a random point with coordinates (x; y): equal probability inside a square whose side is 1 and the center of which coincides with the origin. Determine the probability density of Z = XY


Homework Equations





The Attempt at a Solution

 
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Since the joint density of Z = XY is uniform on the square the probabilities agree with areas. Have you worked out the area corresponding to xy <= z in the square for various z?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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