Login

Search the forums now!

Welcome, Guest. Please login or register.

October 21, 2025, 08:31:55 pm
Pages: [1] 2   Go Down

Author Topic: A Spesh question from me  (Read 4559 times)  Share 

0 Members and 1 Guest are viewing this topic.

Glockmeister

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1660
  • RIP Sweet Nothings.
  • Respect: +8
A Spesh question from me
« on: February 04, 2008, 09:37:04 pm »
0
From my assignment

If , where , show that the number is real only if
« Last Edit: February 11, 2008, 10:53:44 pm by Glockmeister »
Logged
"this post is more confusing than actual chemistry.... =S" - Mao

[22:07] <robbo> i luv u Glockmeister

<Glockmeister> like the people who like do well academically
<Glockmeister> tend to deny they actually do well
<%Neobeo> sounds like Ahmad0
<@Ahmad0> no
<@Ahmad0> sounds like Neobeo

2007: Mathematical Methods 37; Psychology 38
2008: English 33; Specialist Maths 32 ; Chemistry 38; IT: Applications 42
2009: Bachelor of Behavioural Neuroscience, Monash University.

Collin Li

  • VCE Tutor
  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 4957
  • Respect: +17
Re: A Spech question from me
« Reply #1 on: February 04, 2008, 10:04:42 pm »
0
If is real, then and .









For to be real,





Where (as given):







as required.
Logged

enwiabe

  • Putin
  • ATAR Notes Legend
  • *******
  • Posts: 4358
  • Respect: +529
Re: A Spesh question from me
« Reply #2 on: February 04, 2008, 10:11:32 pm »
0
That is a really neat question. Nice working, coblin.
Logged

Collin Li

  • VCE Tutor
  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 4957
  • Respect: +17
Re: A Spesh question from me
« Reply #3 on: February 04, 2008, 10:14:46 pm »
0
Quote from: enwiabe on February 04, 2008, 10:11:32 pm
That is a really neat question. Nice working, coblin.

Thanks. I love complex number questions. In 2006 I had the feeling that I had a comparative advantage in this topic compared to the state. They have a lot of meaning, but it's largely ignored in the VCE syllabus.
Logged

Neobeo

  • Victorian
  • Trendsetter
  • **
  • Posts: 188
  • 反逆 の Neobeo
  • Respect: +3
Re: A Spesh question from me
« Reply #4 on: February 04, 2008, 10:43:20 pm »
0
Alternative solution,

We can rearrange the equation into a quadratic for z, and get
Applying the quadratic formula gives

Since we are given that , must have an imaginary part. Also since is real, it follows that must be imaginary. (Incidentally we also prove that ).

The rest is just basic substitution:

« Last Edit: February 04, 2008, 10:47:22 pm by Neobeo »
Logged
Mathematics Coach: Tuition and Enrichment // Email/MSN:

If you remember the flying birds, they died D=

/0

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 4124
  • Respect: +45
Re: A Spesh question from me
« Reply #5 on: February 04, 2008, 11:04:45 pm »
0
I wish they would say |z| instead of mod z, since it's less ambiguous
Logged

Ahmad

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1296
  • *dreamy sigh*
  • Respect: +15
Re: A Spesh question from me
« Reply #6 on: February 04, 2008, 11:17:05 pm »
0
Quote from: Glockmeister on February 04, 2008, 09:37:04 pm
From my assignment

If , where , show that the number is real only if

Another way. Since ,
Let . (r >= 0)
Then, .
Setting imaginary part equal to zero, since is real, gives
Logged
Mandark: Please, oh please, set me up on a date with that golden-haired angel who graces our undeserving school with her infinite beauty!

The collage of ideas. The music of reason. The poetry of thought. The canvas of logic.

J.Z-M

  • Victorian
  • Adventurer
  • *
  • Posts: 11
  • Respect: 0
Re: A Spesh question from me
« Reply #7 on: February 05, 2008, 10:26:00 am »
0
WOW!
Youse FSN'ers are crazy at maths.
You make it look so simple.
Logged
2006: German(41)

2007: Physical Education(50), Physics(34)

2008:Chemistry(35+), Spec(35+), MM(40+), English(45+)

ENTER 95+ Here I come !!!!

midas_touch

  • Victorian
  • Forum Leader
  • ****
  • Posts: 797
  • Serial Trout Slapper
  • Respect: +4
Re: A Spesh question from me
« Reply #8 on: February 05, 2008, 01:57:18 pm »
0
Coblin's method is great if u really wanna show off ur maths skills.

Ahmad's method is great for an exam situation when u have very little time.
Logged
Some snippets of what goes on in IRC:

Quote
<chath> ill say " i wont let you go until u kiss me bitch"

Quote
<@enwiabe> i have the BEST orgasms when i'm working through a math problem


Quote
<@mark_alec> my bikini line however, is most important

Are you scared yet?

Glockmeister

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1660
  • RIP Sweet Nothings.
  • Respect: +8
Re: A Spesh question from me
« Reply #9 on: February 05, 2008, 07:00:29 pm »
0
Thanks guys

Quote from: DivideBy0 on February 04, 2008, 11:04:45 pm
I wish they would say |z| instead of mod z, since it's less ambiguous

Well... they did, but I couldn't find the LaTeX code for it.

Logged
"this post is more confusing than actual chemistry.... =S" - Mao

[22:07] <robbo> i luv u Glockmeister

<Glockmeister> like the people who like do well academically
<Glockmeister> tend to deny they actually do well
<%Neobeo> sounds like Ahmad0
<@Ahmad0> no
<@Ahmad0> sounds like Neobeo

2007: Mathematical Methods 37; Psychology 38
2008: English 33; Specialist Maths 32 ; Chemistry 38; IT: Applications 42
2009: Bachelor of Behavioural Neuroscience, Monash University.

dcc

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1198
  • Respect: +55
  • School Grad Year: 2008
Re: A Spesh question from me
« Reply #10 on: February 05, 2008, 07:42:59 pm »
0
just put pipes around it (shift + \):

Logged

Glockmeister

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1660
  • RIP Sweet Nothings.
  • Respect: +8
Re: A Spesh question from me
« Reply #11 on: February 05, 2008, 07:52:36 pm »
0
cant seem to get it working
Logged
"this post is more confusing than actual chemistry.... =S" - Mao

[22:07] <robbo> i luv u Glockmeister

<Glockmeister> like the people who like do well academically
<Glockmeister> tend to deny they actually do well
<%Neobeo> sounds like Ahmad0
<@Ahmad0> no
<@Ahmad0> sounds like Neobeo

2007: Mathematical Methods 37; Psychology 38
2008: English 33; Specialist Maths 32 ; Chemistry 38; IT: Applications 42
2009: Bachelor of Behavioural Neuroscience, Monash University.

Collin Li

  • VCE Tutor
  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 4957
  • Respect: +17
Re: A Spesh question from me
« Reply #12 on: February 05, 2008, 09:26:39 pm »
0
Quote from: midas_touch on February 05, 2008, 01:57:18 pm
Coblin's method is great if u really wanna show off ur maths skills.

Ahmad's method is great for an exam situation when u have very little time.

My method is the cookie cutter method. It's the way you would typically go about it. It's the method you'd take if you charge straight ahead into a question. If you are clever, and have the ability to think through a question well (with the aid of some good mathematical intuition), then you can develop more elegant methods like Ahmad's.
Logged

Glockmeister

  • Victorian
  • Part of the furniture
  • *****
  • Posts: 1660
  • RIP Sweet Nothings.
  • Respect: +8
Re: A Spesh question from me
« Reply #13 on: February 05, 2008, 09:29:57 pm »
0
It's probably the most easiest to follow too.
Logged
"this post is more confusing than actual chemistry.... =S" - Mao

[22:07] <robbo> i luv u Glockmeister

<Glockmeister> like the people who like do well academically
<Glockmeister> tend to deny they actually do well
<%Neobeo> sounds like Ahmad0
<@Ahmad0> no
<@Ahmad0> sounds like Neobeo

2007: Mathematical Methods 37; Psychology 38
2008: English 33; Specialist Maths 32 ; Chemistry 38; IT: Applications 42
2009: Bachelor of Behavioural Neuroscience, Monash University.

Collin Li

  • VCE Tutor
  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 4957
  • Respect: +17
Re: A Spesh question from me
« Reply #14 on: February 05, 2008, 09:32:45 pm »
0
That said, it is not to discourage the mere mortals in maths from making clever manipulations like Ahmad's. It is a very good idea to flip the function so that you have a much simpler function. These ideas should always be considered when a lot of algebra is ahead of you.
« Last Edit: February 05, 2008, 09:34:56 pm by coblin »
Logged
Pages: [1] 2   Go Up