AS Further maths: argand diagrams and arguments

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SufferinStudent
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Most of the bloody questions for hw i get states that I have to answer my questions in terms of pi & I don't know pi's significance to the argand diagram!!! Can someone please explain?? :ccc
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PuffyPenguin
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Do you have an example of a question? Pi alone would just be a real component, whereas Pi(i) is an imaginary component
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an_atheist
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(Original post by SufferinStudent)
Most of the bloody questions for hw i get states that I have to answer my questions in terms of pi & I don't know pi's significance to the argand diagram!!! Can someone please explain?? :ccc
Have you covered radians at all in maths? A decent chunk of maths at A Level works in radians rather than degrees, which is where the pi stuff comes from.
Have you covered how to calculate the argument of a complex number?
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SufferinStudent
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(Original post by PuffyPenguin)
Do you have an example of a question? Pi alone would just be a real component, whereas Pi(i) is an imaginary component
Likeeee

write in form a+bi-

4(cos(-5pi /6) + isin(-5pi /6)

How would you do this?
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SufferinStudent
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(Original post by an_atheist)
Have you covered radians at all in maths? A decent chunk of maths at A Level works in radians rather than degrees, which is where the pi stuff comes from.
Have you covered how to calculate the argument of a complex number?
yeah I know how to calculate the argument which is tan= y/x right?

but idk about the radians stuff , do you know where the pi stuff comes from?
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SufferinStudent
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(Original post by SufferinStudent)
yeah I know how to calculate the argument which is tan= y/x right?

but idk about the radians stuff , do you know where the pi stuff comes from?
all i know is that 2pi = 360 degrees when r=1 LOL
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PuffyPenguin
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You can write the sin and cos parts as real numbers, i.e. Cos(-5pi/6) is - root3/2 and sin(-5pi/6) is -1/2. If you sub that in you get -2root 3 -1/2 i
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black1blade
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On the argand diagram complex numbers are represented as vectors.
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black1blade
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The angle between that vector and the positive x-axis is defined as the argument. Going anticlockwise (positive y quadrants) goes from 0to pi and going clockwise (negative y quadrants) goes from 0 to -pi.
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an_atheist
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(Original post by SufferinStudent)
yeah I know how to calculate the argument which is tan= y/x right?

but idk about the radians stuff , do you know where the pi stuff comes from?
The radian is defined as the angle subtended by an arc of length r on a circle of radius r. 2pi radians=360 degrees, as a result. A degree is a slightly nebulous term, so using radians is 'neater' for the purposes of doing maths (as I understand it)
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etothepiiplusone
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(Original post by an_atheist)
using radians is 'neater' for the purposes of doing maths (as I understand it)
Kind of. Radians are the only measure of angle in which \frac{d}{dx} \sin x = \cos x is true, which I suppose does make them 'neater' as opposed to \frac{d}{dx} \sin x ^\circ= \frac{180}{2 \pi} \cos x ^\circ.
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SufferinStudent
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(Original post by black1blade)
The angle between that vector and the positive x-axis is defined as the argument. Going anticlockwise (positive y quadrants) goes from 0to pi and going clockwise (negative y quadrants) goes from 0 to -pi.
so could you treat pi as 180 degrees? are they equivalent?
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PuffyPenguin
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(Original post by PuffyPenguin)
You can write the sin and cos parts as real numbers, i.e. Cos(-5pi/6) is - root3/2 and sin(-5pi/6) is -1/2. If you sub that in you get -2root 3 -1/2 i
(Original post by SufferinStudent)
Most of the bloody questions for hw i get states that I have to answer my questions in terms of pi & I don't know pi's significance to the argand diagram!!! Can someone please explain?? :ccc
See comment above
You can then use a right angled triangle to work out the angle
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black1blade
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(Original post by SufferinStudent)
so could you treat pi as 180 degrees? are they equivalent?
They represent the same thing yes but in pure maths we use radians because they are more useful as pi is an irrational number that is defined in a few ways but it's directly intertwined with how circles work. You'll have to get used to radians sooner or later although I can see why you might be confused because you normally go over radians first in core 2.
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SufferinStudent
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(Original post by PuffyPenguin)
See comment above
You can then use a right angled triangle to work out the angle
ah so you used 180 degrees in substitute of pi to get the 2 values?
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SufferinStudent
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(Original post by black1blade)
They represent the same thing yes but in pure maths we use radians because they are more useful as pi is an irrational number that is defined in a few ways but it's directly intertwined with how circles work. You'll have to get used to radians sooner or later although I can see why you might be confused because you normally go over radians first in core 2.
ah thankss
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