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# complex numbers watch

1. hello!

in polar form of complex numbers, can the angle be negative? can the angle be >360 ?

thanks!
2. (Original post by studos)
hello!

in polar form of complex numbers, can the angle be negative? can the angle be >360 ?

thanks!
strictly speaking no (by convention)
3. should be from -pi to pi i think
in MEI you do it from -pi > theata >/ pi (>/ means greater than or equal to)
4. you both disagree

what is the correct?
5. I suppose technically it could be greater than 360° however the convention is to use values between -pi and pi as this covers all eventualities. If you use an angle greater than 2pi or 360° then it can be simplified to a value between -pi and pi.

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6. (Original post by studos)
you both disagree

what is the correct?
I do not think we disagree

I say it hardly matters ...
if the calculation is mine I can do as I please (in most cases so long as complex logs are involved) since an argument of 13π/6 or π/6 or -11π/6 is the same number.

However the standard convention for the principal argument is -π < argz <=π

(I passed my exams a long time ago so sometimes I do not stick to conventions).
7. so r<-10 is the same with r<350 ?
8. (Original post by studos)
so θ=-10 is the same with θ=350 ?
of course it is

but look at what you are expected to give as answer in your board/module
9. (Original post by ETRC)
should be from -pi to pi i think
in MEI you do it from -pi > theata >/ pi (>/ means greater than or equal to)
how do you expect someone to understand what you wrote?

what is MEI? haven't you learnt that you need to analyze abbreviations before you use them?

also, what is theata? you mean the greek letter theta? you should also indicate that you name the angle of a complex number as theta, because theta could be anything
10. can you tell me please:

why we introduce complex number? what problem do they solve, that we couldn't solve with the rest of maths?

I think one application, is to be able to calculate the sum of sinusoidally changing amounts
but why can't we do that by simply adding vectors? and we have to introduce, j=sqrt(-1), to do it?

thanks!
11. can you tell me please why x<90o (polar form) equals to jx ?

I understand that the 90o degrees, mean that the x vector is on the y axis, which is the imaginary axis

but why this equals j times x? ie. sqrt(-1) times x ?

I mean x can be a real number, like 2, right?

why if that x is on the imaginary number, it becomes sqrt(-1) times 2 ?
12. The reason they use -pi to pi is so that they use
Sin(-x) and cos(-x) rules . In other ranges it may not apply.

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13. (Original post by studos)
how do you expect someone to understand what you wrote?

what is MEI? haven't you learnt that you need to analyze abbreviations before you use them?

also, what is theata? you mean the greek letter theta? you should also indicate that you name the angle of a complex number as theta, because theta could be anything
Who upset you today?

I will try to explain the fellow poster's comments

theata is a place you go watch a play.
M.E.I. stands for M@[email protected] Enhances Intelligence

Happy New Year!

PS is the picure next to the username a picture of yourself?
14. (Original post by TeeEm)
PS is the picure next to the username a picture of yourself?
yes, are you racist?
15. (Original post by studos)
yes, are you racist?
Not at all as I am very foreign myself.
just interest.
16. (Original post by TeeEm)
Who upset you today?

I will try to explain the fellow poster's comments

theata is a place you go watch a play.
M.E.I. stands for M@[email protected] Enhances Intelligence

Happy New Year!

PS is the picure next to the username a picture of yourself?
TeeEmm, you starting the New Years drinking early??

(Original post by studos)

why we introduce complex number? what problem do they solve, that we couldn't solve with the rest of maths?

I think one application, is to be able to calculate the sum of sinusoidally changing amounts
but why can't we do that by simply adding vectors? and we have to introduce, j=sqrt(-1), to do it?

thanks!
Complex numbers let us solve .

(Original post by studos)
can you tell me please why x<90o (polar form) equals to jx ?

I understand that the 90o degrees, mean that the x vector is on the y axis, which is the imaginary axis

but why this equals j times x? ie. sqrt(-1) times x ?

I mean x can be a real number, like 2, right?

why if that x is on the imaginary number, it becomes sqrt(-1) times 2 ?
Write an arbitrary complex number as z=a+bj.

Where ,

Say our complex number was z=j
We then have zero real part.
In polar form, we would have z=1(cos90+jsin90)

Say our complex number was z=4j
In polar form, we would have z=4(cos90+jsin90)

You have to understand that we measure the angle from the positive x-axis line. So if we move along by 90 degrees, we then have no real-part and have only an imaginary part.

Say our complex number was z=-j
In polar form, we would have z=1(cos(-90)+jsin(-90)) = 1(cos270+jsin270)

As mentioned above, it is conventional to use -90<theta<90

Try using Wolfram Alpha and put in some complex numbers to see what their angles would be: http://www.wolframalpha.com/input/?i=-i
I hope this helps.
17. (Original post by rayquaza17)
TeeEmm, you starting the New Years drinking early??
I am drinking right now ...
(I had not started drinking when I typed that comment )
18. thanks!

but why we need to solve . ?
19. (Original post by studos)
how do you expect someone to understand what you wrote?

what is MEI? haven't you learnt that you need to analyze abbreviations before you use them?

also, what is theata? you mean the greek letter theta? you should also indicate that you name the angle of a complex number as theta, because theta could be anything
Good grief. Sort your attitude out or you will find the number of potential helpers will diminish.
20. (Original post by studos)
thanks!

but why we need to solve . ?
http://betterexplained.com/articles/...inary-numbers/

This is pretty much how my lecturer explained it to my class.

BTW: MEI is an exam board, like Edexcel, OCR, AQA. (I am not googling the full names of them to write them out!)

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