Fundamental Theorem of Algebra Can anyone give me a short simple definition of FTOA? 
Every complex polynomial of degree n has exactly n complex roots. if y= ax^n + bx^(n1) + ... z, where a,b,...,z are complex (which includes the reals), y will have n roots (where y =0), each of which is complex. 
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For example, if (23i)x^5  (3+6i)x^3 + (2i)x^2 + i = 0, then there are 5 roots, which are complex? And, if 2x^5  (3i)x^4 + (22i)x^3  6x^2  2 = 0, then there are 5 roots, which are complex...? 
The real numbers are a subset of the complex number system. So any real polynomial (e.g. x^2 + 2x + 1) is a special case of the complex number system. So in answer to your question, it is not necessary that it is not real, just that it is complex. Think of reals as complex numbers where the b in a+bi is 0. a+0i=a. 
Oh yeah, I remember now that a+bi is complex, where not necessary imaginary, because b=0. So, using this knowledge, the Fundamental Theorem of Algebra tells us that if we have a polynomial equal to zero, and its degree n is greater then 0, then it has n roots. Is this correct? 
yes. The root of a polynomial is when the polynomial is equal to zero. So there are n values for which the polynomial is 0 
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a + 0i is real. 0 + bi is imaginary. The only imaginary real number is 0. 
The statement of the theorem should specify "if repeated roots are counted up to their multiplicity". 
well noted, skipjack. 
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