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icystrike
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Homework Statement
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] .
Homework Equations
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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