Question

2-7i over -2+5i solve
2-7i/-2+5i

Answer 1

The general rule of division in the complex set is,

`(a)/(b)=\frac{a\bar{b}}{b\bar{b}}; a,b\in\mathbb{C}`.

If
`b=c+di` than
`\bar{b}=c-di` this is called complex conjugate of a complex number.

We have,

`a=2-7i`

`b=-2+5i`

The complex conjugate of b is
`\bar{b}=-2-5i`.

Now perform the algebra,

`((2-7i)(-2-5i))/((-2+5i)(-2-5i))=(-4-10i-14i+35i^2)/(4+10i-10i-25i^2)`

`=(-4-24i-35)/(4+25)=\boxed{(-39-24i)/(29)}`

In complex form that is,

`-(39)/(29)-(24)/(29)i`

Hope this helps :)