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September 24, 2025, 02:59:32 am
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Author Topic: Why are they not the same?!!!!  (Read 2496 times)  Share 

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TrueTears

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Why are they not the same?!!!!
« on: October 29, 2009, 07:44:04 pm »
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Look at this:





Thus



and are the same ray.

Now check out the sketch:

RAY 1 is

RAY 2 is

They ARE the same line for but for RAY 2 does not extrapolate back to touch the x axis.



So I proved algebraically that they are the exact same ray yet when you sketch they are not?

Why?
« Last Edit: October 29, 2009, 07:49:09 pm by TrueTears »
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NE2000

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Re: Why are they not the same?!!!!
« Reply #1 on: October 29, 2009, 07:50:05 pm »
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Er...yeah TT, correct me if I'm wrong but when you do transformations isn't the translation done after taking the coefficient of z out? So as I said on the other thread, you translate 2 units up first and then rotate.
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TrueTears

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Re: Why are they not the same?!!!!
« Reply #2 on: October 29, 2009, 07:51:34 pm »
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Quote from: NE2000 on October 29, 2009, 07:50:05 pm
Er...yeah TT, correct me if I'm wrong but when you do transformations isn't the translation done after taking the coefficient of z out? So as I said on the other thread, you translate 2 units up first and then rotate.
Checked with kamil on msn just then my way in the other thread is correct just that the answers were stupid (TSFX), they got the domain mixed up.

You translate 2 to the left first and then rotation of 90 deg clockwise.
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TrueTears

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Re: Why are they not the same?!!!!
« Reply #3 on: October 29, 2009, 07:54:21 pm »
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I *think* the reason is splitting up Arg(iz+2) to the the Arg(i) but can't pinpoint it...
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Hooligan

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Re: Why are they not the same?!!!!
« Reply #4 on: October 29, 2009, 08:00:07 pm »
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TT, is this for Exam 1 or 2?  :-\
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TrueTears

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Re: Why are they not the same?!!!!
« Reply #5 on: October 29, 2009, 08:02:46 pm »
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Exam 1 :)
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kamil9876

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Re: Why are they not the same?!!!!
« Reply #6 on: October 29, 2009, 08:18:12 pm »
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sorry, had a massive brain lapse and trusted you're working out :P

Here is how you interpret your (TT's) algebra:

z'=iz+2

z=i^3 (z'-2)

so initially the point get's moved 2 units left, then rotated clockwise 90degrees about ORIGIN 0(the complex number 0). Hence 0 maps to (0,2) as they have done :) and so you get their answer.

However it's actually simpler to expand to z=i^3z' +2i so that u can imagine the transformation easier as simply rotating by 90 degrees first and then translating, this kind of thing is easier to deal with in this situation :)
« Last Edit: October 29, 2009, 08:23:47 pm by kamil9876 »
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TrueTears

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Re: Why are they not the same?!!!!
« Reply #7 on: October 29, 2009, 08:22:07 pm »
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Awesome I totally get it now, thanks kamil (Y)
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Hooligan

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Re: Why are they not the same?!!!!
« Reply #8 on: October 29, 2009, 08:34:52 pm »
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I don't get it.  :-\

How does the transformations work? I know how to do Arg(x+2)= but then adding the just makes it daunting for me...
I know that when you times a complex number by you are rotating it 90 degrees anti-clockwise, but have never come across it in Args....

(side note: whats the order you do transformations in again? I did methods 3/4 last year, and I have completely forgotten. Is it D R T?)
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Over9000

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Re: Why are they not the same?!!!!
« Reply #9 on: October 29, 2009, 08:40:45 pm »
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Quote from: Hooligan on October 29, 2009, 08:34:52 pm
I don't get it.  :-\

How does the transformations work? I know how to do Arg(x+2)= but then adding the just makes it daunting for me...
I know that when you times a complex number by you are rotating it 90 degrees anti-clockwise, but have never come across it in Args....

(side note: whats the order you do transformations in again? I did methods 3/4 last year, and I have completely forgotten. Is it D R T?)
Well generally D R T, but I dont think it works in all situations, your better off judging logically which transformation shud be applied first.
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Hooligan

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Re: Why are they not the same?!!!!
« Reply #10 on: October 29, 2009, 10:37:33 pm »
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Quote from: Over9000 on October 29, 2009, 08:40:45 pm
Quote from: Hooligan on October 29, 2009, 08:34:52 pm
I don't get it.  :-\

How does the transformations work? I know how to do Arg(x+2)= but then adding the just makes it daunting for me...
I know that when you times a complex number by you are rotating it 90 degrees anti-clockwise, but have never come across it in Args....

(side note: whats the order you do transformations in again? I did methods 3/4 last year, and I have completely forgotten. Is it D R T?)
Well generally D R T, but I dont think it works in all situations, your better off judging logically which transformation shud be applied first.

Okay, right... so how do I graph Arg(zi+2)=?
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TrueTears

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Re: Why are they not the same?!!!!
« Reply #11 on: October 29, 2009, 10:39:29 pm »
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http://vcenotes.com/forum/index.php/topic,18491.msg187108.html#msg187108

Make sure the "origin" of the ray as well as the ray gets reflected to look like the RAY 2 in this thread.
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gilla

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Re: Why are they not the same?!!!!
« Reply #12 on: October 29, 2009, 10:46:45 pm »
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Quote from: kamil9876 on October 29, 2009, 08:18:12 pm
sorry, had a massive brain lapse and trusted you're working out :P

Here is how you interpret your (TT's) algebra:

z'=iz+2

z=i^3 (z'-2)

so initially the point get's moved 2 units left, then rotated clockwise 90degrees about ORIGIN 0(the complex number 0). Hence 0 maps to (0,2) as they have done :) and so you get their answer.

However it's actually simpler to expand to z=i^3z' +2i so that u can imagine the transformation easier as simply rotating by 90 degrees first and then translating, this kind of thing is easier to deal with in this situation :)

Hey hru, on the tsfx solutions, they evaluate it is  -pi < 0.5pi + arg(z-2i) < (2pi)/3

then they minus 0.5pi from both sides and sketch. is that right? how come in TT's working he didnt do this?
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TrueTears

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Re: Why are they not the same?!!!!
« Reply #13 on: October 29, 2009, 10:59:22 pm »
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TSFX domain is wrong in this Q.

Kamil's way is perfect, in fact I had it from the start it's just that I didn't rotate the origin of the ray properly.
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NE2000

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Re: Why are they not the same?!!!!
« Reply #14 on: November 01, 2009, 05:09:32 pm »
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Just a question on a similar note. The dotted line that you normally add for inequalities gets rotated around too yeah?

So for

You're gonna have a dotted line at rather than the usual ?
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