# Big Brain Maths Core Pure FM Question

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#1
Please could you help me with this maths question!
Last edited by Professor Ops; 1 month ago
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1 month ago
#2
(Original post by Professor Ops)
Please could you help me with this maths question!
To get started, try sketching an equilateral triangle, including the lines joining the centre to the three vertices. The angles between these three lines are equal and add up to 2(pi).
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#3
(Original post by old_engineer)
To get started, try sketching an equilateral triangle, including the lines joining the centre to the three vertices. The angles between these three lines are equal and add up to 2(pi).
like this?
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1 month ago
#4
(Original post by Professor Ops)
like this?
Yes, now start using trig to find the coordinates of B and C.
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1 month ago
#5
(Original post by old_engineer)
Yes, now start using trig to find the coordinates of B and C.
...or perhaps it might be easier to consider the matrix transformation needed for an anticlockwise rotation of a vector through theta degrees (which is given in the formula booklet).
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1 month ago
#6
(Original post by Professor Ops)
Please could you help me with this maths question!
(a) I'd start with the three roots of unity which form an equiliteral triangle. The three values are easily determined. Then compare the two triangles. One is a scaling and rotation of the other. Consider transforming taking 1+0i to 6+2i. What do you have to multiply the first point by to get that transformation - you should be ble to write that down straight off. Then repeat that transformation with the other two vertices, and you're done.

(b) I'd work with the roots of unity triangle again, and then scale result to the desired triangle.
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1 month ago
#7
Wouldnt it be easier to just work out mod and arg form of 6+2I then add and subtract 2/3pi to the arg and calculate the 2 new complex number?
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1 month ago
#8
(Original post by tej3141)
Wouldnt it be easier to just work out mod and arg form of 6+2I then add and subtract 2/3pi to the arg and calculate the 2 new complex number?
And then convert it back to x+iy format - no, don't think it would be easier. Also, you're asked for the exact values of x,y.
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#9
(Original post by ghostwalker)
And then convert it back to x+iy format - no, don't think it would be easier. Also, you're asked for the exact vasorrlues of x,y.
sorry for the late reply and thanks for your help. I still have no idea what to do sorry
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1 month ago
#10
(Original post by Professor Ops)
sorry for the late reply and thanks for your help. I still have no idea what to do sorry
The key regarding the equilateral triangle of the cube roots of unity, is that when you multiply by a given complex number, call it z, geometrically you scale your initial number by |z|, and rotate it by arg(z). So, going from the cube roots of unity equilateral triangle, you get to your desired triangle, by a simple multiplication.
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1 month ago
#11
(Original post by Professor Ops)
sorry for the late reply and thanks for your help. I still have no idea what to do sorry
Actually a simpler method for (a). Forget my previous posts. To get the other two points, you can rotate your initial point by 120 degrees. So, what complex number (multiplied) corresponds to a rotation of 120 degrees?

And area can be obtained just by looking at the intial point and making some deductions - geometrically!
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1 month ago
#12
(Original post by Professor Ops)
Please could you help me with this maths question!
Sorry just wondering, where's this question from? 😭
Last edited by Qxi.xli; 1 month ago
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