.
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°).
Solved, answered and explained.
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There is a bunch of my lessons on complex numbers
- Complex numbers and arithmetical operations on them
- Complex plane
- Addition and subtraction of complex numbers in complex plane
- Multiplication and division of complex numbers in complex plane
- Raising a complex number to an integer power
- How to take a root of a complex number
- Solution of the quadratic equation with real coefficients on complex domain
- How to take a square root of a complex number
- Solution of the quadratic equation with complex coefficients on complex domain
- Solved problems on taking roots of complex numbers
- Solved problems on arithmetic operations on complex numbers
- Solved problem on taking square root of complex number
- Miscellaneous problems on complex numbers
- Advanced problem on complex numbers
- Solved problems on de'Moivre formula
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Complex numbers".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.