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

i)Find the fourth roots of the complex number -1+[tex]\sqrt{3}i[/tex] , giving your answer in the form of r[tex]e^{i\theta}[/tex] .

ii)Deduce the solution of the equation [tex]z^{8}+2z^{4}+4=0[/tex] , giving your answer exactly in the form r[tex]e^{i\theta}[/tex] .

2. Relevant equations

3. The attempt at a solution

i)[tex]2^{\frac{1}{4}}e^{(1+3k)\frac{\pi}{6}i}[/tex]

s.t [tex]k=0,\pm1,2[/tex]

ii)[tex]z^{4}=-1\pm\sqrt{3}i[/tex]

z=[tex]2^{\frac{1}{4}}e^{(1+3k)\frac{\pi}{6}i}[/tex]

or

z=[tex]2^{\frac{1}{4}}e^{(-1+3k)\frac{\pi}{6}i}[/tex]

[tex]k=0,\pm1,2[/tex]

They have only included the conjugate case.

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# Homework Help: Complex Number agn.

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