SOLUTION: What are the fifth roots of -32i?

Notice that  -32i = .


Therefore, due to DeMoivre formulas, the 5-th degree roots of -32i are



    (1)  2cis(54°);     ( notice that 54° =  );


    (2)   = = 2cis(54° + 72°) = 2cis(126°);    ( Notice that 72° =  )


    (3)   = 2cis(54° + 2*72°) = 2cis(198°);


    (4)   = 2cis(54° + 3*72°) = 2cis(270°);


    (5)   = 2cis(54° + 4*72°) = 2cis(342°).