SOLUTION: Does anyone know if there is a quick way to solve the type of problem below? I know I can use de moivre's theorem, but it takes me a while. Not necessarily looking for the solution

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Question 1091281: Does anyone know if there is a quick way to solve the type of problem below? I know I can use de moivre's theorem, but it takes me a while. Not necessarily looking for the solution to this particular problem, just want to know if there is a faster way to do it than de moivre's theorem. Thanks!

Problem: Find the three cube roots of -7+5i and express the roots in polar coordinates.
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
Properly use deMoivre's formula is the unique way to solve this problem.

It is unique and it is quite fast (fast enough).

So, learn it and use it.


Good luck and happy learning !


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There is a bunch of 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
    - A curious example of an equation in complex numbers which HAS NO a solution
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".