Proving Non-Linearity of y2: Linear Operators Homework

spaghetti3451
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Homework Statement



Show that y2 is non-linear.


Homework Equations



^O (ay1 +by2) = a ^O(y1) + b ^O(y2).

The Attempt at a Solution



No idea!
 
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I have no idea what you mean by "^0".
Is it the operation (here, squaring)?

Then replace it by squaring: is (ay_1+ by_2)^2= ay_1^2+ by_2^2?
 
Thanks for the clue! I've solved the problem now!
 

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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