Results 1 to 7 of 7

Math Help - Parametric curves and complex numbers

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    130

    Parametric curves and complex numbers

    Hello guys, i've done a few more problems that i need corrected, thanks.

    1.) The position of a particle in the xy plane at time t (seconds) is given by r(t) = (2 + 5t^2)i + (-3 + t)j

    a) find the cartesian equation of the particles trajectory

    my answer: x = 5y^2 + 30y +47

    b) Sketch the particles trajectory also indicating its direction of motion

    my solution: the shape of the graph x = 5y^2 + 30y + 47 is a sideways parabola with a vertex at (2,-3) which was found by completing the square. the particle is travelling in the direction to increase y.

    __________________________________________________ ______________________

    2.) Write the following complex numbers in cartesian form x + iy where x and y are real numbers.

    a) (2 - 3i) / (2i - 1)

    my solution: -i/8 - 8/3

    b) (3-2i)^2 (1+5i)

    my solution: 75 + 13i

    __________________________________________________ ______________________

    3.) Find the modulus and argument of z = - (root3)/(10) - 1/10i between -pi and pi.

    my solution: arg(z) = - 5pi/6
    modulus (z) = 1/5

    __________________________________________________ _________________________
    thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Parametric curves and complex numbers

    Ex 2:
    a) Almost correct, you made a mistake in the denominator, it has to be:
    \frac{2-3i}{2i-1}=\frac{(2-3i)(2i+1)}{(2i-1)(2i+1)}=\frac{4i-6i^2+2-3i}{-4-1}=\frac{i+8}{-5}=\frac{-i}{5}-\frac{8}{5}

    b) Also here you made a little mistake:
    (3-2i)^2\cdot (1+5i)=(9-12i-4)\cdot (1+5i)=(5-12i)\cdot (1+5i)=5+25i-12i-60i^2=5+13i+60=65+13i

    Ex 3:
    Correct!
    You can do the check by yourself, if \mbox{arg}(z)=\frac{-5\pi}{6} and \mbox{mod}(z)=\frac{1}{5} then the complex number is:
    \frac{1}{5}\cdot \left[\cos\left(\frac{-5\pi}{6}\right)+i\sin\left(\frac{-5\pi}{6}\right)\right]=
    \frac{-\sqrt{3}}{10}-\frac{i}{10}=z
    Last edited by Siron; September 3rd 2011 at 03:10 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: Parametric curves and complex numbers

    Quote Originally Posted by andrew2322 View Post
    1.) The position of a particle in the xy plane at time t (seconds) is given by r(t) = (2 + 5t^2)i + (-3 + t)j

    a) find the cartesian equation of the particles trajectory my answer: x = 5y^2 + 30y +47

    b) Sketch the particles trajectory also indicating its direction of motion my solution: the shape of the graph x = 5y^2 + 30y + 47 is a sideways parabola with a vertex at (2,-3) which was found by completing the square. the particle is travelling in the direction to increase y.
    Right.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: Parametric curves and complex numbers

    Quote Originally Posted by andrew2322 View Post
    3.) Find the modulus and argument of z = - (root3)/(10) - 1/10i between -pi and pi.
    my solution: arg(z) = - 5pi/6 modulus (z) = 1/5
    Right.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jan 2008
    Posts
    130

    Re: Parametric curves and complex numbers

    thanks guys, much appreciated.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,553
    Thanks
    1422

    Re: Parametric curves and complex numbers

    Quote Originally Posted by andrew2322 View Post
    Hello guys, i've done a few more problems that i need corrected, thanks.

    1.) The position of a particle in the xy plane at time t (seconds) is given by r(t) = (2 + 5t^2)i + (-3 + t)j

    a) find the cartesian equation of the particles trajectory

    my answer: x = 5y^2 + 30y +47

    b) Sketch the particles trajectory also indicating its direction of motion

    my solution: the shape of the graph x = 5y^2 + 30y + 47 is a sideways parabola with a vertex at (2,-3) which was found by completing the square. the particle is travelling in the direction to increase y.

    __________________________________________________ ______________________

    2.) Write the following complex numbers in cartesian form x + iy where x and y are real numbers.

    a) (2 - 3i) / (2i - 1)

    my solution: -i/8 - 8/3

    b) (3-2i)^2 (1+5i)

    my solution: 75 + 13i

    __________________________________________________ ______________________

    3.) Find the modulus and argument of z = - (root3)/(10) - 1/10i between -pi and pi.

    my solution: arg(z) = - 5pi/6
    modulus (z) = 1/5

    __________________________________________________ _________________________
    thanks in advance.
    You should write 1. a) as y in terms of x if possible.

    \displaystyle \begin{align*} 5y^2 + 30y + 47 &= x \\ y^2 + 6y + \frac{47}{5} &= \frac{x}{5} \\ y^2 + 6y + 3^2 + \frac{47}{5} &= \frac{x}{5} + 3^2 \\ \left(y + 3\right)^2 + \frac{47}{5} &= \frac{x + 45}{5} \\ \left(y + 3\right)^2 &= \frac{x - 2}{5} \\ \left(y + 3\right)^2 &= \frac{5(x - 2)}{25} \\ \left(y + 3\right)^2 &= \frac{5x - 10}{25} \\ y + 3 &= \pm \frac{\sqrt{5x - 10}}{5} \\ y &= \frac{-15 \pm \sqrt{5x-10}}{5}\end{align*}
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: Parametric curves and complex numbers

    Quote Originally Posted by Prove It View Post
    You should write 1. a) as y in terms of x if possible.
    I can't guess why we should write y in terms of x .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help on Parametric Curves please
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 10th 2010, 12:02 PM
  2. Parametric curves
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 14th 2010, 01:56 PM
  3. Parametric Curves
    Posted in the Calculus Forum
    Replies: 9
    Last Post: October 20th 2009, 06:14 PM
  4. Parametric Curves
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 6th 2009, 10:34 PM
  5. Parametric Curves
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 25th 2007, 03:35 PM

Search Tags


/mathhelpforum @mathhelpforum