Clock Hands: 180 Degree Angle in 24 Hours

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Homework Statement



Hi , How Many Times in A day 2 of 3 clock hands makes the angle of 180 degree with each other ?
 
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I Just Find This Formula :

Angle BetWeen Min And Hour Is : ANGLE = 30H - (11/2)M

But I Do'nt Know how to solve it And Find the H And M That ANGLE=180 ;
 

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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