SOLUTION: I have to write the complex expression in rectangular standard form: (square root -3 + i)^6 Any idea how you write it in standard form?

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Question 1053022: I have to write the complex expression in rectangular standard form: (square root -3 + i)^6
Any idea how you write it in standard form?
Found 2 solutions by KMST, ikleyn:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%28-3%29+%2Bi%29%5E6 ? %28sqrt%283%29%2Bi%29%5E6 ?

%28sqrt%283%29%2Bi%29%5E6 has more charm as a problem,
because sqrt%283%29%2Bi has a real part, sqrt%283%29 and an imaginary part 1%2Ai ,
so it begs for using the polar form.
r=sqrt%28%28sqrt%283%29%29%5E2%2B1%5E2%29=sqrt%283%2B1%29=sqrt%284%29=2
tan%28theta%29=1%2Fsqrt%283%29=sqrt%283%29%2F3 , so system+%28theta=pi%2F6%2C%22or%22%2Ctheta=pi%2Bpi%2F6%29 ,
but since sqrt%283%29%3E0 and 1%3E0 , it must be theta+=pi%2F6 , in the first quadrant.
So, sqrt%283%29%2Bi=2%28cos%28pi%2F6%29%2Bi%2Asin%28pi%2F6%29%29 and
%28sqrt%283%29%2Bi%29%5E6=2%5E6%28cos%28pi%29%2Bi%2Asin%28pi%29%29=64%28-1%2Bi%2A0%29=-64 .

is a real number,
but from then on it gets complicated.
=-%284%2B2sqrt%283%29%29%5E3
=

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
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
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.