#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)))