Results 1 to 3 of 3

Thread: Reciprocal of Complex Number?

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    79

    Reciprocal of Complex Number?

    $\displaystyle z=\frac{3+4i}{2-3i}$. What is the complex number which satisfies the equation $\displaystyle zw=1$.

    My attempt:

    $\displaystyle \begin{array}{rcrcrc}
    z=\frac{3+4i}{2-3i}\\
    \\
    zw=1\\
    \\
    w=\frac{1}{z}\\
    \\
    \frac{3+4i}{2-3i}*\frac{2+3i}{2+3i}=\frac{-6+17i}{13}
    \end{array}$

    Is it right up to there? If so, I see I need to get the reciprocal of that (which will be the value of w). How would I do that?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Matt Westwood's Avatar
    Joined
    Jul 2008
    From
    Reading, UK
    Posts
    1,281
    Thanks
    197
    Quote Originally Posted by Viral View Post
    $\displaystyle z=\frac{3+4i}{2-3i}$. What is the complex number which satisfies the equation $\displaystyle zw=1$.

    My attempt:

    $\displaystyle \begin{array}{rcrcrc}
    z=\frac{3+4i}{2-3i}\\
    \\
    zw=1\\
    \\
    w=\frac{1}{z}\\
    \\
    \frac{3+4i}{2-3i}*\frac{2+3i}{2+3i}=\frac{-6+17i}{13}
    \end{array}$

    Is it right up to there? If so, I see I need to get the reciprocal of that (which will be the value of w). How would I do that?
    My initial utterly naive approach would be to say that $\displaystyle 1/(a/b) = b/a$ and so $\displaystyle w = 1/z = \frac{2-3i}{3+4i}$.

    Or am I missing something subtle?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    79
    Ahh, I was trying to do that after working it out >< . I didn't think it would make a difference. Thanks, I'll try that out.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex number
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 7th 2010, 11:31 AM
  2. Replies: 1
    Last Post: Oct 2nd 2010, 01:54 PM
  3. Replies: 3
    Last Post: Sep 13th 2010, 11:13 AM
  4. Replies: 1
    Last Post: Nov 10th 2008, 09:25 AM
  5. Reciprocal of a complex number
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Jan 16th 2008, 04:34 PM

Search Tags


/mathhelpforum @mathhelpforum