DeMoivre's theorem
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Suppose we want to find the nth root of a complex number z; that is, we
want to find w such that
We write z and w in the form
Using DeMoivre's theorem we have (using the equation )
i) Show that the absolute value of wn and z are equal. Hence find R in terms of r.
ii) Equate the arguments of wn and z to find a general expression for y in terms of x.
iii) Write down the general formula for the nth root of z.
iv) Hence find all solutions of the equation 11/4=w.
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Solution Summary
DeMoivre's theorem is clearly evaluated in this case.
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