Question

find the fifth roots of -32i

Answers

Mariam
Notice that -32i = 2%5E5%2Acis%28270%5Eo%29.


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



(1) 2cis(54°); ( notice that 54° = 270%5Eo%2F5 );


(2) 2cis%2854%5Eo+%2B+360%5Eo%2F5%29 = = 2cis(54° + 72°) = 2cis(126°); ( Notice that 72° = )


(3) 2cis%2854%5Eo+%2B+2%2A%28360%5Eo%2F5%29%29 = 2cis(54° + 2*72°) = 2cis(198°);


(4) 2cis%2854%5Eo+%2B+3%2A%28360%5Eo%2F5%29%29 = 2cis(54° + 3*72°) = 2cis(270°);


(5) 2cis%2854%5Eo+%2B+4%2A%28360%5Eo%2F5%29%29 = 2cis(54° + 4*72°) = 2cis(342°).

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