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Finding The Cube Root(s) of 18 + 26i | Problem 287 

aplusbi
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24 авг 2024

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Комментарии : 9   
@SweetSorrow777
@SweetSorrow777 Месяц назад
Writing the problem in polar form could produce those other solutions.
@ibnSafaa
@ibnSafaa Месяц назад
you can easliy use the cubic roots of unity (w , w² , 1) x³=a³ ∴x=a , x=aw , x=aw²
@DonRedmond-jk6hj
@DonRedmond-jk6hj Месяц назад
How does your cube root formula compare with DeMoivre's formula?
@krabbediem
@krabbediem Месяц назад
Loved it! Thank you :D
@mikelivstone
@mikelivstone Месяц назад
Do the second and third solutions correspond to the 2 remaining values of t at 3:53? That avenue was not really pursued.
@bkkboy-cm3eb
@bkkboy-cm3eb Месяц назад
α=³√(18+26i), β=³√(18-26i) α³+β³=36 α³β³=1000 → αβ=10 (α+β)³=α³+β³+3αβ(α+β) α+β=t → t³-30t-36=0 (t-6)(t²+6t+6)=0 → t=6 ∴α+β=6, αβ=10 → α²-6α+10=0 ∴α=3+i α₁=α·e^(i2π/3) α₂=α·e^(i4π/3) ∴α=3+i, (-3-√3+(3√3-1)i)/2, (3+√3+(1-3√3)i)/2
@Nobodyman181
@Nobodyman181 Месяц назад
a,b,t,k Too many constant 😅
@phill3986
@phill3986 Месяц назад
😊😊😊👍👍👍
@scottleung9587
@scottleung9587 Месяц назад
Cool!
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