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# Argand Diagrams watch

1. can somebody please give me a reason why these exist. i know they represent a complex number interns of another but there has to be a better reeason to using them
thx
Ben
2. (Original post by XXXNICEGUYXXX)
can somebody please give me a reason why these exist. i know they represent a complex number interns of another but there has to be a better reeason to using them
thx
Ben
to shade things, to calculate areas of triangles easier? stuff like that
3. Why do numbers exist? Because we invented them to serve a purpose...
4. (Original post by XXXNICEGUYXXX)
can somebody please give me a reason why these exist. i know they represent a complex number interns of another but there has to be a better reeason to using them
thx
Ben
It helps us express complex numbers in another form, something about the argument of a complex number. I think that's degree level stuff.
5. (Original post by ZJuwelH)
It helps us express complex numbers in another form, something about the argument of a complex number. I think that's degree level stuff.
nope argurment is p4 and its very easy... usually: arg(z)=arctan(b/a) where z=a+bi and arg(z) has to be between pi and -pi... argand diagrams make it easier to work out the arg as you can see which sector the complex number is in and therefore what numbers you have to use with arctan...
6. (Original post by S1M)
nope argurment is p4 and its very easy... usually: arg(z)=arctan(b/a) where z=a+bi and arg(z) has to be between pi and -pi... argand diagrams make it easier to work out the arg as you can see which sector the complex number is in and therefore what numbers you have to use with arctan...
Fair enough, I managed to avoid P4 and P5. So can any number of complex numbers have the same argument?
7. (Original post by ZJuwelH)
Fair enough, I managed to avoid P4 and P5. So can any number of complex numbers have the same argument?
yes if they are positive factors of each other... ie z=a+bi and nz=n(a+bi) will have the same arg... but i dont think -nz will have the same arg... that would have (argz - pi) as the argurment
8. So why do we need the argument of a complex number again? lol
Does it just represent the trig. ratio of the real part to the im part?
9. (Original post by mik1a)
So why do we need the argument of a complex number again? lol
Does it just represent the trig. ratio of the real part to the im part?
something like that... im not sure if it has a use in p4... they just say calculate the argument of this....
10. Maybe it's a joke, just to fill the syllabus up! lol. they just made up some words like they used to in SATs : "the strechyness of a box is given by s = root(5t /(1-4cb^2)) where s = .... if the strechyness is 19.7, find s"

Anyway.

I bet there's something to do with calculus in there... you can never escape it! Especially when you're dealing with arguments (tan arg z is just the gradient of the vector z isnt it?)...
11. The argument is useful because you can express a complex number in the form z = re^ix where x is the argument. This form can then be used with demoivre's theorem to do all manner of things, a few things i've learnt is quickly finding expressions for things like sin7x in terms of sinx, or even more commonly than that roots of unity. This comes back to the argand diagram (as if it wasn't pretty enough), because the nth roots of 1 form pretty geometric shapes on the argand diagram.

ANNNNNNND, the fact that the argand diagram is a plane which features all sorts of geometry makes it useful for other results which I haven't actually studied but have heard about. And it all tends to come from the fact that multiplying something by i rotates it 90 degrees on the argand diagram.
12. (Original post by mik1a)
Maybe it's a joke, just to fill the syllabus up! lol. they just made up some words like they used to in SATs : "the strechyness of a box is given by s = root(5t /(1-4cb^2)) where s = .... if the strechyness is 19.7, find s"

Anyway.

I bet there's something to do with calculus in there... you can never escape it! Especially when you're dealing with arguments (tan arg z is just the gradient of the vector z isnt it?)...
well some of those questions were funny... some university lecturers have similar humour and you might find funny questions in your uni exams... when you go to uni...

not sure if calculus has anything to do with it though...
13. (Original post by fishpaste)
The argument is useful because you can express a complex number in the form z = re^ix where x is the argument. This form can then be used with demoivre's theorem to do all manner of things, a few things i've learnt is quickly finding expressions for things like sin7x in terms of sinx, or even more commonly than that roots of unity. This comes back to the argand diagram (as if it wasn't pretty enough), because the nth roots of 1 form pretty geometric shapes on the argand diagram.

ANNNNNNND, the fact that the argand diagram is a plane which features all sorts of geometry makes it useful for other results which I haven't actually studied but have heard about. And it all tends to come from the fact that multiplying something by i rotates it 90 degrees on the argand diagram.
14. (Original post by S1M)
I'm not done yet ! ...anddddd if you were in the business of proving fermat's last theorem you'd probably want to use modular forms, and to understand modular forms you have to understand what is meant by a periodic complex function and as far as I know complex functions are just like real ones except they have an imaginary component of the graph perpendicular to the real component, ie. mapped on the argand plane. And soooo without the argand diagram you wouldn't even be able to solve fermat's last theorem. *shudders at the mere thought of it* [/********]
15. (Original post by fishpaste)
I'm not done yet ! ...anddddd if you were in the business of proving fermat's last theorem you'd probably want to use modular forms, and to understand modular forms you have to understand what is meant by a periodic complex function and as far as I know complex functions are just like real ones except they have an imaginary component of the graph perpendicular to the real component, ie. mapped on the argand plane. And soooo without the argand diagram you wouldn't even be able to solve fermat's last theorem. *shudders at the mere thought of it* [/********]
lol... im not gonna read that... im happy with my explaination:
the point of doing it is because it gets you marks and its easy

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