# Argand Diagrams

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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

thx

Ben

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#2

(Original post by

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

**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

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#4

**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

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#5

(Original post by

It helps us express complex numbers in another form, something about the argument of a complex number. I think that's degree level stuff.

**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.

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#6

(Original post by

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...

**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...

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#7

(Original post by

Fair enough, I managed to avoid P4 and P5. So can any number of complex numbers have the same argument?

**ZJuwelH**)Fair enough, I managed to avoid P4 and P5. So can any number of complex numbers have the same argument?

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#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?

Does it just represent the trig. ratio of the real part to the im part?

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#9

(Original post by

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?

**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?

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#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"

Lol... they made me laugh.

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?)...

Lol... they made me laugh.

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?)...

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#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.

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.

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#12

(Original post by

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"

Lol... they made me laugh.

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?)...

**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"

Lol... they made me laugh.

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?)...

not sure if calculus has anything to do with it though...

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#13

(Original post by

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.

**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.

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#14

(Original post by

well theres your P6/degree explaination

**S1M**)well theres your P6/degree explaination

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#15

(Original post by

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* [/bull****]

**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* [/bull****]

*the point of doing it is because it gets you marks and its easy*

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