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Math Help - Complex Number Division. Easy

  1. #1
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    Complex Number Division. Easy

    \frac{z_{2}}{z_{1}} , z_{1} = 2 + 3i, z_{2} = 4 - 5i

    \frac{4-5i}{2+3i}

     <br />
\frac{x_{1}x_{2}+y_{1}y_{2}}{x_{2}^{2}+y_{2}^{2}} + i\frac{x_{1}y_{2}-x_{2}y_{1}}{x_{2}^{2}+y_{2}^{2}} <br />

    \frac{4*2+(-5)*3}{4+9} + i\frac{4*3-2*(-5)}{4 + 9}

    \frac{8-15}{13} + i\frac{12+10}{13}

    \frac{-7}{13} + i\frac{22}{13}

    Answer in the book is \frac{-7}{13} - i\frac{22}{13} and it says nothing about a conjugate
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  2. #2
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    Quote Originally Posted by Fallen186 View Post
    \frac{z_{2}}{z_{1}} , z_{1} = 2 + 3i, z_{2} = 4 - 5i

    \frac{4-5i}{2+3i}
    In the numerator  (4-5i)(2-3i)=8-12i-10i+15i^2=-22i-7<br />
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