On my final today, there was the question that no nonreal complex number has a nth real root.

I know this is true but I wasn't able to prove it.

Another question was, Let S be a finite set where z=a+bi. Prove S is bounded.

For this one, I said since S is finite, S is can be put in a 1-1 correspondence with .

Also, I was allowed to assume .

I then said .

Now, we have .

So S must be bounded. I know it is wrong but how should it be done or what could I have added or altered to make it correct?