Results 1 to 5 of 5

Math Help - Reciprocal of a complex number

  1. #1
    Member
    Joined
    Dec 2007
    Posts
    98

    Question Reciprocal of a complex number

    I am asked to solve this

    \frac{10}{3-4i}

    I looked over the book to see how this is done...

    according to the book

    \frac{1}{3+4i} is to be written in stnrd form a+bi, so then one must multiply both the denominator and numerator by the opposite of the denominator in this case 3-4i.

    \frac{1}{3+4i}.\frac{3-4i}{3-4i}= \frac{3-4i}{9+16}

    Ok here is where I don't get it, what happened(s) to the i and the signs in the denominator of \frac{3-4i}{9+16}

    is the multiplication process of the denominator the same as using foil?! or am I just full of complex numbers!?


    \frac{3-4i}{9+16} = \frac{3}{25}-\frac{4}{25} i

    Where did the 25 come from?!

    Thanks in advance to all!!

    Last edited by Morzilla; January 15th 2008 at 07:16 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,670
    Thanks
    298
    Awards
    1
    Quote Originally Posted by Morzilla View Post
    I am asked to solve this

    \frac{10}{3-4i}

    I looked over the book to see how this is done...

    according to the book

    \frac{1}{3+4i} is to be written in stnrd form a+bi, so then one must multiply both the denominator and numerator by the opposite of the denominator in this case 3-4i.

    \frac{1}{3+4i}.\frac{3-4i}{3-4i}= \frac{3-4i}{9+16}

    Ok here is where I don't get it, what happened(s) to the i and the signs in the denominator of \frac{3-4i}{9+16}

    is the multiplication process of the denominator the same as using foil?! or am I just full of complex numbers!?


    \frac{3-4i}{9+16} = \frac{3}{25}-\frac{4}{25} i

    Where did the 25 come from?!

    Thanks in advance to all!!

    Yes, you FOIL out the denominator as if "i" were a variable.

    (3 + 4i)(3 - 4i) = 9 - 12i + 12i - 16i^2 = 9 - 16i^2 = 9 + 16

    (Or you could just note that this is a (a + b)(a - b) = a^2 - b^2 form.)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Dec 2007
    Posts
    98
    Quote Originally Posted by topsquark View Post
    Yes, you FOIL out the denominator as if "i" were a variable.

    (3 + 4i)(3 - 4i) = 9 - 12i + 12i - 16i^2 = 9 - 16i^2 = 9 + 16

    (Or you could just note that this is a (a + b)(a - b) = a^2 - b^2 form.)

    -Dan
    and what about the 25 in the denominator, where did come from?!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Awards
    1
    Quote Originally Posted by Morzilla View Post
    and what about the 25 in the denominator, where did come from?!
    (3+4i)(3-4i) = 9 -16i^2 \Rightarrow 9 - (-16) = 9 + 16 \Rightarrow 25
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Dec 2007
    Posts
    98
    Quote Originally Posted by colby2152 View Post
    (3+4i)(3-4i) = 9 -16i^2 \Rightarrow 9 - (-16) = 9 + 16 \Rightarrow 25
    yes, a math tutor showed me this in the math lab......boy I felt like such a Duh!

    Much Thanks!!

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 2nd 2010, 01:54 PM
  2. Replies: 3
    Last Post: September 13th 2010, 11:13 AM
  3. Reciprocal of Complex Number?
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 10th 2009, 06:28 AM
  4. complex number
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: June 14th 2009, 05:15 AM
  5. Replies: 1
    Last Post: November 10th 2008, 09:25 AM

Search Tags


/mathhelpforum @mathhelpforum