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andrethisman88
02.03.2020 •
Mathematics
Find the cube roots of 27(cos 330 + i sin 330)
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Ответ:
answer:
the cube roots of 27(cos 330° + i sin 330°) will be
∛[27(cos 330° + i sin 330°)]
we know that
e^(ix)=cos x + isinx
therefore
∛[27(cos 330° + i sin 330°)]> ∛[27(e^(i330°))]> 3∛[(e^(i110°)³)]
3∛[(e^(i110°)³)]> 3e^(i110°)> 3[cos 110° + i sin 110°]
z1=3[cos 110° + i sin 110°]
cube root in complex number, divide angle by 3
360nº/3 = 120nº --> add 120º for z2 angle, again for z3
therefore
z2=3[cos ((110°+120°) + i sin (110°+120°)] > 3[cos 230° + i sin 230°]
z3=3[cos (230°+120°) + i sin (230°+120°)]> 3[cos 350° + i sin 350°]
the answer is
z1=3[cos 110° + i sin 110°]
z2=3[cos 230° + i sin 230°]
z3=3[cos 350° + i sin 350°]
Step-by-step explanation:
Ответ:
1
Step-by-step explanation:
lol im dumb i havent learnt these yet-