Complex Number Division. Easy

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December 16th 2009, 03:30 PM
Fallen186

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
December 16th 2009, 03:47 PM
pickslides

Quote:

Originally Posted by Fallen186

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

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

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

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