Question

Question #7d38c

Answer 1

As written `10/10+5i=color(blue)(1+5i)`

Probably what was intended: `10/(10+5i)=color(magenta)(4/5-2/5i)`

Explanation:

As written
`color(white)("XXX")10/10+5i`
`color(white)("XXX")=(cancel(10)^1)/(cancel(10)_1)+5i`

`color(white)("XXX")=1+5i`

If the expression was intended to be `color(black)(10/(10+5i)`
`color(white)("XXX")10/(10+5i)`

`color(white)("XXX")=10/(10+5i)xx(10-5i)/(10-5i)color(white)("xxxxx")`using the complex conjugate of the denominator

`color(white)("XXX")=(100-50i)/(100-(-25))`

`color(white)("XXX")=(100-50i)/(125)`

`color(white)("XXX")=(4-2i)/5`