(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve: [tex]x^3 + 4\sqrt{1+i} = 0[/tex]

and express in both cartesian and polar form.

2. Relevant equations

[tex]e^{i\theta} = \cos (\theta) + i \sin (\theta)[/tex]

3. The attempt at a solution

What I did was move the constant term to the right hand side and squared both sides to get: [tex]x^6 = 16 + 16 i[/tex]

which implies: [tex]x = (16+16i)^{1/6} = \left[16\sqrt{2}\right]^{1/6} e^{\frac{(8k+1)\pi i}{6}}[/tex]

Then I simply sub in k = 0, 1, .., 5 for all my roots. But the original equation is a polynomial of degree 3. There should be only 3 factors. Do I have to test them all to see if they work? Or is there an easier way...

Thanks.

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# Homework Help: Solve (complex) equation

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