 | In[4]:=
ComplexExpand[x^100 + a*x^50 + b /. {x -> 1/2 + (I*Sqrt[3])/2}]
ComplexExpand[{Re[%], Im[%]}]
Out[4]=-(1/2) - a/2 + I*(-(Sqrt[3]/2) + (Sqrt[3]*a)/2) + b
Out[5]={-(1/2) - a/2 + b, -(Sqrt[3]/2) + (Sqrt[3]*a)/2}
In[6]:=Solve[% == {0, 0}, {a, b}]
Out[6]={{b -> 1, a -> 1}}
<--零点をx^100 + a*x^50 + bに代入し,
実部、虚部 零 で コタエ
---------------おまけ；---------------
In[7]:=
x^100 + a*x^50 + b /. {b -> 1, a -> 1}
Factor[%]
Out[7]=
1 + x^50 + x^100
Out[8]=
(1 - x + x^2)*(1 + x + x^2)*
(1 - x + x^3 - x^4 + x^5 - x^7 + x^8)*
(1 + x - x^3 - x^4 - x^5 + x^7 + x^8)*
(1 - x^5 + x^15 - x^20 + x^25 - x^35 +
x^40)*(1 + x^5 - x^15 - x^20 - x^25 +
x^35 + x^40)
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