Asked by joe
                find the fifth roots of -32i
            
            
        Answers
                    Answered by
            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°).
    
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°).
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.