Not sure if its me or the book error but I had a complex number question
(6+i)(a+bi)=2
My solution for
My book has a different solution to that.
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I spent 5 minutes on this and couldn't solve it.
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I think my book has done another mistake. (The book has made a few mistakes so I'm just checking with people on here)
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i got an
x+yi
my x-component was :
I haven't solved the y-component yet. Want to get 'x' right before I do the y.
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The book's answer is right, you can check it by squaring it to get 5 + i.
x^2 - y^2 + 2xyi = 5+i
Comparing real and imaginary
2xy = 1
y = 1/2x
x^2 - y^2 = 5
x^2 - 1/4x^2 = 5
4x^4 - 20x^2 - 1 = 0
x^2 = (20 +- sqrt(20^2 - 4(4)(-1))/2(4)
x^2 = (20+- sqrt(416))/8
x^2 = (20 +- 4sqrt(26))/8
x^2 = (5 +- sqrt(26))/2
But x is real so take the positive case only
x = +- sqrt[(5+sqrt26)/2]
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apologies if the question isn't clear (hence my two examples)
Last edited by jathu123; 10 Sep 2017 at 7:41 PM. Reason: Fixed typo
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Last edited by seanieg89; 15 Sep 2017 at 5:29 PM.
Is there a formula for finding the sum of all points (angles where it's spiky) on an n pointed star? For example, for a 5 pointed star, it is 180 degrees
For higher n, there becomes multiple ways to construct the star, each with their own angle sum. ie. the points of the star may create an n-gon, or another star, as shown for n = 7, 11. Note in each case, the first star creates an n-gon by joining every second vertex, while the others create other stars.
Last edited by 1729; 25 Sep 2017 at 6:24 PM.
This may not be in the spirit of the question, but if you had something different in mind with a more geometric proof, I'd like to see it. Let be the centre of circle . Consider the kite , and apply the cosine rule to the side from both and . Letting, . We obtain that, . A similar expression is obtained for . From this we obtain,
. As we have that is monotonic increasing, and so is maximised if and only if is maximised. Using the appropriate formulae we obtain,
, through calculus or the AM-GM inequality we obtain a maxima when that is unique and so on. However this sends suggesting that .
Last edited by Sy123; 6 Oct 2017 at 5:08 PM.
In how many ways can seven identical cats be put into three identical pens so that all of the pens are occupied? You must state reasoning. (2 marks)
Why can we not use stars and bars? I.e. 9C2
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Here is a useful article for placing n identical objects into r identical bins: https://brilliant.org/wiki/identical...identical-bins .
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