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in polar form makes this trivial.
. Here 
is the inverse tangent function that takes into account position in the coordinate plane; look up "atan2" for more information)
and 
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If [tex]z=-1-\sqrt{3}i[/tex] and [tex]z^{6}=a+bi[/tex], then [tex]a[/tex] = _ and [tex]b[/tex] = _...
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