[tex]7) \frac{2-i}{2+i} = \frac{(2-i)^2}{2^2-i^2}= \frac{4-4i+i^2}{5}= \frac{3}{5}- \frac{4}{5}i \\ I \frac{3}{5}- \frac{4}{5}iI= \sqrt{( \frac{3}{5})^ 2+( \frac{4}{5})^2 }= \sqrt{1}=1 \\ 8)(3-2i)(4+5i)=12+7i-10=2+7i \\ I2+7iI= \sqrt{4+49}= \sqrt{53} \\ 9) \frac{4(3+2i)}{9+4}+ \frac{4(3-2i)}{9+4}= \frac{24}{13} [/tex]
