Results 1 to 2 of 2

Thread: Solving another equation

  1. #1
    Super Member
    Joined
    Dec 2008
    Posts
    509

    Solving another equation

    Hi i need help on where i have gone wrong in the following equations:
    1)Solve $\displaystyle (x+2i)(x-2i)=5-12i $ for real values x and y.
    $\displaystyle x^2+2ix+2ix+4i^2=5-12i$

    $\displaystyle x^2+4ix-4=5-12i$

    $\displaystyle x^2+4ix=9-12i$

    $\displaystyle 4ix+12i=9-x^2$

    $\displaystyle i(4x+12)=9-x^2$

    $\displaystyle 4x+12=9-x^2$

    $\displaystyle x^2+4x+3$

    $\displaystyle (x-1)(x+3)$
    x=1 or x=-3

    2)Solve $\displaystyle (x+iy)(x+iy)=-18i$ for real values x and y.
    $\displaystyle x^2+ixy+ixy+i^2y^2=-18i$

    $\displaystyle x^2+2ixy-y^2=-18i$

    $\displaystyle 2ixy-18i=x^2-y^2$

    $\displaystyle i(2xy-18)=y^2-x^2$

    Also another question does $\displaystyle -i^2=1$ and $\displaystyle i^2=-1$

    P.S
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    For 2

    a complex number z = 0 if and only if Re(z) = 0 and Im(z) =0

    (x^2 - y^2) + i (2xy -18) = 0

    x^2 = y^2 x = + y

    and 2xy = 18

    If x= y 2x^2 = 18 x= +3

    If x = -y -2x^2 =18 and there are no solutions

    only solutions are (3,3) and (-3,-3)

    For 1)

    (x+2i)(x-2i) = x^2 + 2ix - 2ix - 4i^2 = x^2 + 4

    also

    Even if

    how do you conclude 4x+12 = 9 -x^2 ?

    you should have x^2 + 4 = 5 -12 i

    x^2 = 1-12i

    if x is real x^2 must be real so there are no solutions


    yes i^2 =-1 and -i^2 = 1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving equation for x
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: Jul 2nd 2011, 05:17 PM
  2. Solving an equation.
    Posted in the Pre-Calculus Forum
    Replies: 10
    Last Post: Nov 6th 2010, 04:46 PM
  3. Solving Equation
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Aug 7th 2010, 06:46 AM
  4. solving diff equation w/ bournoulli's equation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 14th 2008, 06:06 PM
  5. Help on solving equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Jul 26th 2007, 04:01 PM

Search Tags


/mathhelpforum @mathhelpforum