Page 2 of 7 FirstFirst 1234 ... LastLast
Results 26 to 50 of 155
Like Tree28Likes

Thread: HSC 2018 MX2 Marathon

  1. #26
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    99
    Rep Power
    3

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by pikachu975 View Post
    So let z = x + 2i

    (x+2i)^2 = x^2 + 4xi - 4
    Since it is real then Im(z^2) = 0
    so 4x = 0
    x = 0

    Hence z = 2i
    thank you Pikachu!!

  2. #27
    Cadet
    Join Date
    Oct 2015
    HSC
    2018
    Gender
    Female
    Posts
    99
    Rep Power
    3

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by pikachu975 View Post
    So let z = x + 2i

    (x+2i)^2 = x^2 + 4xi - 4
    Since it is real then Im(z^2) = 0
    so 4x = 0
    x = 0

    Hence z = 2i
    how about if re(z) is 2Im(z) and z^2-4i is real

    I cant get the answer.. the answer is +- (2+i)

  3. #28
    Junior Member 1729's Avatar
    Join Date
    Jan 2017
    HSC
    2018
    Gender
    Male
    Location
    Sydney
    Posts
    198
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by sssona09 View Post
    how about if re(z) is 2Im(z) and z^2-4i is real

    I cant get the answer.. the answer is +- (2+i)
    Last edited by 1729; 8 Nov 2017 at 10:09 PM.
    sssona09 likes this.

  4. #29
    -insert title here- Paradoxica's Avatar
    Join Date
    Jun 2014
    HSC
    2016
    Gender
    Male
    Location
    Outside reality
    Posts
    2,456
    Rep Power
    5

    Re: HSC 2018 MX2 Marathon

    Prove the ellipses:



    where k is an arbitrary real number

    have the same area as the ellipse

    Last edited by Paradoxica; 20 Nov 2017 at 12:53 AM.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  5. #30
    Cadet
    Join Date
    Apr 2015
    HSC
    2019
    Gender
    Male
    Posts
    46
    Rep Power
    3

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by Paradoxica View Post
    Prove the ellipses:



    have the same area as the ellipse

    Continuing on, prove that the area of the ellipse defined by



    has area


  6. #31
    This too shall pass Sy123's Avatar
    Join Date
    Nov 2011
    HSC
    2013
    Gender
    Male
    Posts
    3,733
    Rep Power
    8

    Re: HSC 2018 MX2 Marathon




  7. #32
    -insert title here- Paradoxica's Avatar
    Join Date
    Jun 2014
    HSC
    2016
    Gender
    Male
    Location
    Outside reality
    Posts
    2,456
    Rep Power
    5

    Re: HSC 2018 MX2 Marathon

    Letting the value of the solution to x = cos(x) be r, the following area expressions are obtained through integration:

    A₁ = sin(r) - r²/2

    A₂ = 1 - sin(r) + r²/2

    A₂ - A₁ = 1 - 2sin(r) + r²

    r > sin(r) (proof is trivial and left as an exercise)

    - 2sin(r) > - 2r

    1 - 2sin(r) + r² > 1 - 2r + r² = (1-r)² > 0

    A₂ - A₁ > 0

    A₂ > A₁
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  8. #33
    New Member
    Join Date
    Jul 2016
    HSC
    2018
    Gender
    Male
    Posts
    8
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon


  9. #34
    Senior Member sida1049's Avatar
    Join Date
    Jun 2013
    HSC
    2015
    Gender
    Male
    Posts
    751
    Rep Power
    4

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by Pakka View Post
    Change to polar form, apply de Moivre's theorem, done. For all of them.

    Bachelor of Science (Advanced Mathematics) III, USYD

  10. #35
    New Member
    Join Date
    Jul 2016
    HSC
    2018
    Gender
    Male
    Posts
    8
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Could show me some working pls. Sorry for the trouble

  11. #36
    New Member
    Join Date
    Jul 2016
    HSC
    2018
    Gender
    Male
    Posts
    8
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Never mind, I got it. Cheers, the advice made things easier.
    sida1049 likes this.

  12. #37
    New Member
    Join Date
    Jul 2016
    HSC
    2018
    Gender
    Male
    Posts
    8
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    This one pls
    Capture 3.JPG

  13. #38
    I love trials pikachu975's Avatar
    Join Date
    May 2015
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    2,403
    Rep Power
    4

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by Pakka View Post
    This one pls
    Capture 3.JPG
    Realise the denominator and use De Moivre's at the end to get the n in 2ntheta
    --------------------------------------------------------------------------------

    Buy my books/notes cheaply here!

    --------------------------------------------------------------------------------

    Uni Course: Actuarial Studies and Statistics at MQ -- PM me if you have questions

    2017 HSC Subjects: Eng Adv / 3u+4u Maths / Bio /Phys
    ATAR: 99.75

    --------------------------------------------------------------------------------

  14. #39
    New Member
    Join Date
    Jul 2017
    HSC
    2018
    Gender
    Male
    Posts
    8
    Rep Power
    1

    Re: HSC 2018 MX2 Marathon

    Appreciate some help with this: Find the range of values of |z| and arg(z) for |z-4-4i|=2sqrt(2)

  15. #40
    Junior Member 1729's Avatar
    Join Date
    Jan 2017
    HSC
    2018
    Gender
    Male
    Location
    Sydney
    Posts
    198
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by CapitalSwine View Post
    Appreciate some help with this: Find the range of values of |z| and arg(z) for |z-4-4i|=2sqrt(2)
    Sketch the locus of z and note that the modulus and argument of z use the join of the origin to a point on the circle.

  16. #41
    New Member
    Join Date
    Jul 2017
    HSC
    2018
    Gender
    Male
    Posts
    8
    Rep Power
    1

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by 1729 View Post
    Sketch the locus of z and note that the modulus and argument of z use the join of the origin to a point on the circle.
    What is the modulus and argument of z in this case? I got an answer that was different to the one in the textbook.

    Sent from my Redmi Note 4 using Tapatalk

  17. #42
    Cadet altSwift's Avatar
    Join Date
    Jan 2017
    HSC
    2018
    Gender
    Male
    Posts
    65
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Find an expression for cos^4x in terms of cos4x and cos2x

    Edit: The question is from terry lee so I'm guessing it implies that you use 4U complex techniques rather than 3U, I'm not sure if you can even use 3U for this...

  18. #43
    Rambling Spirit
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    6,085
    Rep Power
    7

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by altSwift View Post
    Find an expression for cos^4x in terms of cos4x and cos2x

    Edit: The question is from terry lee so I'm guessing it implies that you use 4U complex techniques rather than 3U, I'm not sure if you can even use 3U for this...

















  19. #44
    Loquacious One
    Join Date
    Feb 2009
    HSC
    N/A
    Gender
    Male
    Posts
    3,754
    Rep Power
    10

    Re: HSC 2018 MX2 Marathon

    Therefore, using 3U method:

    Last edited by Drongoski; 10 Jan 2018 at 8:34 PM.
    1-on-1 Maths Tutoring(IB & HSC): Epping, Beecroft, Eastwood, Carlingford & Beyond
    IB: Maths Studies, Maths SL & Maths HL; HSC: 2U, 3U & 4U
    Highly Qualified & Highly Experienced. Estimated ATAR > 9.995
    There are IB Maths Tutors and there are IB Maths Tutors.

  20. #45
    Taking a break! dan964's Avatar
    Join Date
    Jun 2014
    HSC
    2014
    Uni Grad
    2018
    Gender
    Male
    Location
    South of here
    Posts
    2,947
    Rep Power
    5

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by CapitalSwine View Post
    What is the modulus and argument of z in this case? I got an answer that was different to the one in the textbook.

    Sent from my Redmi Note 4 using Tapatalk
    It is is circle of radius centred at 4+4i.

    The construction is as follows
    Join the points 4+4i (centre C) and origin O, extend this line so that it touches the circle again at B. This line OB will give us the range of values for |z|

    To find the arg z, construct a diagram, observe the points E and F where the arg z is max and min, form a right angled triangle. The ratios of the sides will give the external angles, and from there using symmetry, the angles formed by the tangent at E and F at the origin, gives the max and min of the arg z.

    In this problem |z| is from
    and arg z is from

  21. #46
    Cadet altSwift's Avatar
    Join Date
    Jan 2017
    HSC
    2018
    Gender
    Male
    Posts
    65
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by InteGrand View Post
















    I understand the 3U method, and I understand the proof for the 4U method, I'm just stumped as to how ur supposed to continue with the 4U method, I seem to be going around in circles lmao

  22. #47
    Junior Member fluffchuck's Avatar
    Join Date
    Apr 2016
    HSC
    2017
    Gender
    Male
    Location
    Sydney
    Posts
    241
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by altSwift View Post
    I understand the 3U method, and I understand the proof for the 4U method, I'm just stumped as to how ur supposed to continue with the 4U method, I seem to be going around in circles lmao
    Last edited by fluffchuck; 20 Jan 2018 at 11:33 PM.

  23. #48
    Taking a break! dan964's Avatar
    Join Date
    Jun 2014
    HSC
    2014
    Uni Grad
    2018
    Gender
    Male
    Location
    South of here
    Posts
    2,947
    Rep Power
    5

    Re: HSC 2018 MX2 Marathon

    next question:

    using demoivre's theorem or some other complex number theorems, find the exact value of cos 36 degrees.
    go...

  24. #49
    Cadet altSwift's Avatar
    Join Date
    Jan 2017
    HSC
    2018
    Gender
    Male
    Posts
    65
    Rep Power
    2

    Re: HSC 2018 MX2 Marathon

    Quote Originally Posted by fluffchuck View Post
    ah that makes more sense. we haven't done binomial expansions yet so looks like ill have to do it the long way haha

  25. #50
    Cadet
    Join Date
    Feb 2018
    HSC
    2018
    Gender
    Male
    Posts
    69
    Rep Power
    1

    Re: HSC 2018 MX2 Marathon

    z= x+iy, w = u+iv; w = z -1/z. , find locus of w if |z|=2
    edit:from patel textbook

Page 2 of 7 FirstFirst 1234 ... LastLast

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •