# Complex Number Division. Easy

• Dec 16th 2009, 04:30 PM
Fallen186
Complex Number Division. Easy
$\frac{z_{2}}{z_{1}} , z_{1} = 2 + 3i, z_{2} = 4 - 5i$

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

$
\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}}
$

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

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

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

Answer in the book is $\frac{-7}{13} - i\frac{22}{13}$ and it says nothing about a conjugate
• Dec 16th 2009, 04:47 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
$