The general rule of division in the complex set is,
[tex]\frac{a}{b}=\dfrac{a\bar{b}}{b\bar{b}}; a,b\in\mathbb{C}[/tex].
If [tex]b=c+di[/tex] than [tex]\bar{b}=c-di[/tex] this is called complex conjugate of a complex number.
We have,
[tex]a=2-7i[/tex]
[tex]b=-2+5i[/tex]
The complex conjugate of b is [tex]\bar{b}=-2-5i[/tex].
Now perform the algebra,
[tex]\dfrac{(2-7i)(-2-5i)}{(-2+5i)(-2-5i)}=\dfrac{-4-10i-14i+35i^2}{4+10i-10i-25i^2}[/tex]
[tex]=\dfrac{-4-24i-35}{4+25}=\boxed{\dfrac{-39-24i}{29}}[/tex]
In complex form that is,
[tex]-\dfrac{39}{29}-\dfrac{24}{29}i[/tex]
Hope this helps :)
