Question 986069
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See the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/complex/How-to-take-a-root-of-a-complex-number.lesson>How to take a root of a complex number</A>&nbsp; in this site.


<B>Answer</B>. &nbsp;One root is &nbsp;&nbsp;{{{z[1]}}} = 4*(cos(115°) + i*sin(115°)) &nbsp;&nbsp;&nbsp;&nbsp;(notice that &nbsp;115° = {{{1/2}}}.330°). 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The other root is &nbsp;&nbsp;{{{z[2]}}} = 4*(cos(115°+180°) + i*sin(115°+180°)) = 4*(cos(295°) + i*sin(295°)). &nbsp;&nbsp;&nbsp;&nbsp;(Notice that &nbsp;180° = {{{1/2}}}.360°).


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Also notice that {{{z[2]}}} = {{{-z[1]}}}.