Results 1 to 4 of 4

Math Help - quadratic equations with imaginary numbers

  1. #1
    edm
    edm is offline
    Newbie
    Joined
    Jul 2009
    Posts
    6

    quadratic equations with imaginary numbers

    I am doing some work with z transforms which are littered with quadratics, but I am slightly confused about a fundamental when solving a quadratics with an imaginary component.

    2s^2-2s+1 = 0

     \frac{2\pm\sqrt{-4}} {4} = \frac{2\pm2j} {4} = \frac{1} {2} \pm \frac{1}{2}j

    thats fine. no problem. its next example which has me confused,

    s^2 + 2s + 5 = 0

    \frac {-2\pm \sqrt{-16}} {10} = \frac {-2 \pm 4j} {10} = -\frac{1}{5} \pm \frac{2}{5}j

    but the answer should be,

    -1 \pm 2j

    so what happens to the denominator?

    thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,658
    Thanks
    1615
    Awards
    1
    Quote Originally Posted by edm View Post
    its next example which has me confused,

    s^2 + 2s + 5 = 0

    \frac {-2\pm \sqrt{-16}} {{\color{red}10}} = \frac {-2 \pm 4j} {{\color{red}10}} = -\frac{1}{5} \pm \frac{2}{5}j

    but the answer should be, so what happens to the denominator? -1 \pm 2j
    The denominator is 2 not 10.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Stroodle's Avatar
    Joined
    Jun 2009
    Posts
    367
    Remember that the denominator in the quadratic formula is 2a from the general quadratic equation ax^2+bx+c=0
    Follow Math Help Forum on Facebook and Google+

  4. #4
    edm
    edm is offline
    Newbie
    Joined
    Jul 2009
    Posts
    6
    ah bloody hell thats why it made no sense, i took the s or a 5 .

    thats the problem when you scribble down Ss 2s and Zs they all look the same (well in my hand writing anyway!).

    many thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Primes in Imaginary Quadratic field
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: March 10th 2010, 04:26 AM
  2. Imaginary, quadratic
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: March 8th 2010, 04:18 PM
  3. Quadratic equation with imaginary roots
    Posted in the Algebra Forum
    Replies: 8
    Last Post: January 5th 2010, 01:51 AM
  4. Imaginary numbers/complex numbers
    Posted in the Algebra Forum
    Replies: 7
    Last Post: August 25th 2009, 11:22 AM
  5. Complex Numbers- Imaginary numbers
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 24th 2007, 12:34 AM

Search Tags


/mathhelpforum @mathhelpforum