SOLUTION: (1+i) to the 100th. I have a TI-89 that will solve this and the answer is -1.1259E15 but how was the solution derived?
Algebra.Com
Question 464918: (1+i) to the 100th. I have a TI-89 that will solve this and the answer is -1.1259E15 but how was the solution derived?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
If we were to expand the whole thing,
^{100} = (100C0) + (100C1)i - (100C2) - (100C3)i + (100C4) + ... - (100C98) - (100C99)i + (100C100))
We see that the real part is
^{100}) = (100C0) - (100C2) + (100C4) - ... + (100C100))
and the imaginary part is
^{100}) = (100C1)i - (100C3)i + (100C5)i - ... + (100C97)i - (100C99)i)
All of the imaginary terms cancel out, because we can group the terms together, noting that nCk = nC(n-k):
i - (100C99)i) + (-(100C3)i + (100C97)i) + ... = 0 + 0 + 0 +... = 0)
Hence, we are left with the real part, which happens to be that real number you posted.
RELATED QUESTIONS
1/x+1/y=1/z solve for x. I have seen the answer, x=yz/y-z. I need to know how the answer... (answered by scott8148)
This problem seems very simple but I have been stuck on it for 20 minutes and I don't... (answered by checkley71,jecegc)
I am trying to use logarithms to find the fifth root of 37.
The procedure I used gives... (answered by venugopalramana)
hi. i have a test coming up and i was wondering if you could check this problem for me.
(answered by richwmiller)
Hi!
I have been trying to use old, retired ACT exams to prepare to take the actual... (answered by josgarithmetic,MathLover1,MathTherapy)
Hi
I am having great difficulty trying to solve the following:-
I have tried puting (answered by amylouise93,jim_thompson5910)
When I try to graph or solve for (x)^(1/3) or other odd roots, I get a complex number... (answered by Earlsdon)
I'm studying for an assessment test and this is not a good start. I'm now feeling anxiety (answered by edjones,MathLover1)
I will first describe the picture. There is a rectangle, ABCD with the long side labeled... (answered by edjones)