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Solve the equation z^6=-i |
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Answer» Solution :`Z^6=-i=COS(3pi)/2+ISIN(3pi)/2` `=cos((3pi)/2+2kpi)+isin((3pi)/2+2kpi)` `cos(PI(4k+3))/2+isin(pi(4k+3))/2` `z=[(cos(4k+3)pi)/2=isin((4k+3)pi)/2]^(1/6)` `cos((4k+3)pi)/(12)=isin((4k+3)pi)/(12)` `"where "k=0,2,3,4,5` |
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