+118729 
+118729 Hi Gibsonj335,
Find all sixth roots of (-64)
the first one is 2i this has no real part so it is on the imaginary axis. it is \(2e^{i\pi/2}\)
the difference in the angles (arguments) is going to be 2pi/6
the angles will be
So the first angle is pi/2 which equals 3pi/6
the angles (arguments) will be
\( \frac{3\pi}{6},\quad \frac{3\pi+2\pi}{6},\quad \frac{3\pi+4\pi}{6},\quad \frac{3\pi+6\pi}{6},\quad \frac{3\pi+8\pi}{6},\quad \frac{3\pi+10\pi}{6}\\~\\ \frac{3\pi}{6},\quad \frac{5\pi}{6},\quad \frac{7\pi}{6},\quad \frac{9\pi}{6},\quad \frac{11\pi}{6},\quad \frac{13\pi}{6}\\~\\ \mbox{so the 6 roots will be:}\\~\\ 2e^{\frac{3\pi i}{6}},\quad 2e^{\frac{5\pi i}{6}},\quad 2e^{\frac{7\pi i}{6}},\quad2e^{ \frac{9\pi i}{6}},\quad 2e^{\frac{11\pi i}{6}},\quad 2e^{\frac{13\pi i}{6}}\\~\\ \)
I wasn't sure of the working so I used this for a reference:
http://tutorial.math.lamar.edu/Extras/ComplexPrimer/Forms.aspx
