Can someone provide a solution for this "Complex number"

[ericawat]

[2+3i]\frac{a}{b}[/i(4-5i)] + [2]\frac{a}{b}[/i]

solve in the form a+b, ab = realNumber



or use this if the built in editor doesn't works
2+3i 2
------ + -
i(4-5i) i

[Baltuilhe]

Solution!

[tex]\frac{2+3i}{4-5i}+\frac{2}{i}[/tex]

[tex]\frac{2+3i}{4-5i}\cdot\frac{4+5i}{4+5i}+\frac{2}{i}\cdot\frac{-i}{-i}[/tex]

[tex]\frac{8-15+(10+12)i}{16+25}+\frac{-2i}{1}[/tex]

[tex]\frac{-7+22i}{41}-2i[/tex]

[tex]\frac{-7+22i}{41}-\frac{82i}{41}[/tex]

[tex]\frac{-7-60i}{41}=-\frac{7}{41}-\frac{60i}{41}[/tex]