Tuesday, 19 April 2016

Can some one explain to me what is going on here - power of complex number



So here is the question and the work to solve it, but I have no idea how one knows to do the first step or what the first step is...



(6i12)12=[48(cos(π6)isin(π6))]12=(48)12[cos(12π6)isin(12π6)]=486


Answer



Step 1 Write your number in polar coordinates, i.e. z=r(cost+isint).



Step 2 Use De Moivre's theorem, that (cost+isint)n=cosnt+isinnt.


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