Using De-Moiver's Method Find fourth root of -64.

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we wish to find ( – 64)^1/4 or 2root2*( – 1)^1/4 . we write – 1 as e^ipi or e^i(pi+2kpi). so ( – 1)^1/4= e^i[(pi+2kpi)/4], where k can take values {0, 1, 2, 3}. note that we can convert e^i[(pi+2kpi)/4] into a+ib form once again, by using e^ix=cosx + isinx formula. hence we will obtain 4 distinct roots, one of which is real while rest being complex roots.