SOLUTION: (2-i)^6 the ‘i’ is the imaginary number can someone please help? this is my last problem for my homework on UMTYMP thanks UMTYMP: university of minnesota talente

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Question 1158353: (2-i)^6
the ‘i’ is the imaginary number
can someone please help?
this is my last problem for my homework on UMTYMP
thanks
UMTYMP: university of minnesota talented youth mathematics program
Found 4 solutions by MathLover1, ikleyn, greenestamps, my_user_id:
Answer by MathLover1(20849) About Me  (Show Source):
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

I, naively, always thought that talented young students always seek the solutions to their problems on their own.


It looks like the times just changed significantly . . .


If not to say, radically, cardinally and dramatically . . .



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution from the other tutor uses several multiplications to arrive at the (correct) answer.

My preference is to use binomial expansion:
(1)(2^6) + (6)(2^5)(-i) + (15)(2^4)((-i)^2) + 20(2^3)((-i)^3) + 15(2^2)((-i)^4) + 6(2)((-i)^5) + (-i)^6
   64    +   (-192i)    +      (-240)       +     160i        +        60       +    (-12i)    +   (-1)

= -117 - 44i

Answer by my_user_id(3) About Me  (Show Source):
You can put this solution on YOUR website!
-117-44i or i guess you can write it as 117+44i :)