Complexity Is Awesome!
The equation
x
1
0
+
(
1
3
x
−
1
)
1
0
=
0
has
1
0
complex roots:
r
1
,
r
1
,
r
2
,
r
2
,
r
3
,
r
3
,
r
4
,
r
4
,
r
5
,
r
5
,
where the bar denotes complex conjugation. Evaluate the expression below.
r 1 r 1 1 + r 2 r 2 1 + r 3 r 3 1 + r 4 r 4 1 + r 5 r 5 1
Image Credit: Wikimedia Decagon by László Németh
The answer is 850.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
2 solutions
Could you please elaborate?
It is repeated question. I won't tell the question since one can see the answer from one question, and put it in another.
You would need a pen and a paper to understand properly.....this is just a hint of complete solution. ...........((13x-1)/x)^10 + 1 = 0.......let it be z^10 + 1 =0........then solutions of 'z' are e^(i(2n+1)Π/10) ......where n is any integer in the range -5<=n<=4........from 'z' we get x= 1/(13-z)......then the term belonging to the summation of the series asked is "(13-z)(13-conjugate of z)"......adding corresponding terms we get the sum the series asked as 850.