Mathematics
frankhee
2016-04-17 21:50:36
Find the cube roots of 125(cos 288° + i sin 288°)
ANSWERS
LeBurkhart
2016-04-18 00:19:51

let r(cos O + i sin O)  be a cube root of 125(cos 288 + i sin 288) then r^3(cos O + i sin O)^3  =  125(cos 288 + i sin 28) so r^3 = 125  and  cos 3O + i sin 3O  =  cos 288 + i sin 288 so r  = 5  and 3O = 288 + 360p and O = 96 +  120p so one cube root is   5 (cos 96 + i sin 96) Im a little rusty at this stuff Its been a long time. Im not sure of the other 2 roots sorry cant help you any more

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