1.

Solve the equation z^3=i

Answer»

Solution :`Z^3=i=COS((3pi)/2)+ISIN((3pi)/2)`
`=cos(2kpi+PI/2)+isin (2kpi+pi/2)`
`=cos(pi(4k+1))/2 +sin(pi(4k+1))/2`
`:.z=[cos((4k+1))/2+isin((4k+1)pi)/2]^(1/3)
`=cos((4k+1)pi)/6+isin((4k+1)pi)/6`
`"where" k=0,1,2.`


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