1.

Solve the equation z^6=-i

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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