SOLUTION: Find all solutions of the equation x^4 - 625i = 0 I have 625i = 625cis(90) 4th roots = 5cis(90/4), 5cis(450/4), 5cis(810/4) and 5cis(1170/4) = 5(cos(22.5) + isin(22.5)) are t

Algebra ->  Test  -> Lessons -> SOLUTION: Find all solutions of the equation x^4 - 625i = 0 I have 625i = 625cis(90) 4th roots = 5cis(90/4), 5cis(450/4), 5cis(810/4) and 5cis(1170/4) = 5(cos(22.5) + isin(22.5)) are t      Log On


   

Question 1077713: Find all solutions of the equation x^4 - 625i = 0
I have
625i = 625cis(90)
4th roots = 5cis(90/4), 5cis(450/4), 5cis(810/4) and 5cis(1170/4) = 5(cos(22.5) + isin(22.5))
are these results displayed "graphically?" If not, please help me make them so.
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
The 4-th roots of 625*i are these four numbers:


1)  5%2A%28cos%2890%2F4%29+%2B+i%2Asin%2890%2F4%29%29


2)  5%2A%28cos%2890%2F4+%2B+90%29+%2B+i%2Asin%2890%2F4%2B90%29%29


3)  5%2A%28cos%2890%2F4+%2B+180%29+%2B+i%2Asin%2890%2F4%2B180%29%29


4)  5%2A%28cos%2890%2F4+%2B+270%29+%2B+i%2Asin%2890%2F4%2B270%29%29.

See the lessons
    - How to take a root of a complex number
    - Solved problems on taking roots of complex numbers
in this site.

There is a bunch of lessons on complex numbers in this site
    - Complex numbers and arithmetic 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

    - OVERVIEW of lessons on complex numbers


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".


To display them graphically, use the sketch of the circle of the radius 5 and mark these points in the circle.