BlakeJA@ Posted January 24, 2006 Share Posted January 24, 2006 I was asked this question and it has stumped me for a week so i figured i'd come ask you all to see if anyone knows how to solve it. let p(z) = z^n + iz^(n-1) - 10 if wi are the roots of this polynomial where i= 1,2,3,...,n Compute: Sum(wj) from j=1 to n Product(wj) from j=1 to n where sum is capital Sigma (summation) and product is capital pi (product) and the j is a subscript and Z is a complex number Link to comment Share on other sites More sharing options...

Tartaglia Posted January 24, 2006 Share Posted January 24, 2006 Expanding (z-w0)*(z-w1)*(z-w2)* ...*(z-wn-1) = z^n -(w0+w1+w2+w3 ....+wn-1)z^(n-1) + (-1)^n*(w0*w1*w2*... *wn-1) with all other coefficients of z less than n-1 being zero. equating coefficents i = -(w0+w1+....+wn-1) -10 = (-1)^n* (w0*w1*w2*...wn-1) therefore sum of roots = -i, product = -10 if n is even or +10 if n is odd Link to comment Share on other sites More sharing options...

blakeja Posted January 24, 2006 Share Posted January 24, 2006 awesome, thanks so much i knew it was something simple that i was missing Link to comment Share on other sites More sharing options...

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