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
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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)
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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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