Question

Question #3f656

Answer 1

`color(red)(""(-6+sqrt(2)))+color(blue)(""(2sqrt(6)+sqrt(3)))i`

Explanation:

Noting that `sqrt(-2)=sqrt(2)i`
the multiplication can be done in several ways.
Here it is in tabular form:

`ul(color(white)("x")xxcolor(white)("xx")"|"color(white)("xx")-sqrt(3)color(white)("xx")+sqrt(2)i)`
`+2sqrt(3)"|"color(white)("xxx")-6color(white)("xxxx")+2sqrt(6)i`
`ul(color(white)("x")-icolor(white)("xx")"|"color(white)("xx")+sqrt(3)icolor(white)("xxx")+sqrt(2))`
`-6+sqrt(2)color(white)("x")+color(white)("x")2sqrt(6)i+sqrt(3)i`
or
`color(red)(""(-6+sqrt(2)))+color(blue)(""(2sqrt(6)+sqrt(3)))i`