#1) Find a polynomial equation of Degree 5 with roots {1,5i,1+i,?,?}
#1) ANS: roots are {1,5i,1+i,-5i,1-i}
#1) ANS: factors are (x-1),(x-5i),(x-(1+i)),(x+5i)(x-(1-i))
#1) ANS: x^5-3*x^4+29*x^3-77*x^2+100*x-50==0
show(expand((x-5*i)*(x+5*i)))
show(expand(x-(1+i))*(x-(1-i)).simplify_radical())
show(expand((x+i-1)*(x-i-1)))
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show(expand((x-1)*(x^2+25)))
show(expand((x^3-x^2+25*x-25)*(x^2-2*x+2)))
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factor(x^5-3*x^4+29*x^3-77*x^2+100*x-50)
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solve(x^5-3*x^4+29*x^3-77*x^2+100*x-50==0,x)
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plot(x^5-3*x^4+29*x^3-77*x^2+100*x-50,-2,2)
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