Robert C.

asked • 12/07/14

Find all complex number solutions for x^3+i=0.

Find all complex number solutions for x^3+i=0.

2 Answers By Expert Tutors

By:

Mark M. answered • 12/07/14

Tutor
5.0 (243)

Mathematics Teacher - NCLB Highly Qualified

At A.

Why cos [(1/3)(3π/2)]= cosπ/2?
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02/21/21

Mark M.

Christopher,
 
Please instruct me. Euler's formula is eiπ + 1 = 0, or e = -1. Why am I missing the "/2?"
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12/07/14

Christopher R.

tutor
e=cos(Π)+i*sin(Π)=-1+i*0=-1   eiΠ/2=cos(Π/2)+i*sin(Π/2)=0+i*1=i  Mark M is correct. I totally forgot De Moivre's Theorem. Thanks Mark M. 
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12/07/14

Mark M.

You're welcome.
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12/07/14

Christopher R.

tutor
I just checked my answer to see if it would work. Here it is:
(√3/2-i*1/2)3 = (√3/2)3-3(√3/2)2*i*1/2+3(√3/2)*(i*1/2)2-(i*1/2)3
                     =3√3/8-3*3/4*i*1/2+3√3/2*i2*1/4-i3/8
                     =3√3/8-i*9/8-3√3/8+i*1/8 
                     =-i*8/8=-i  Hence, my answer also works. Therefore, there are two answers to this problem.
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12/07/14

Mark M.

Christopher, 
 
Yes, complex roots always come in conjugate pairs.
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12/08/14

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