Question

Write the expression in standard form. five divided by quantity three minus fifteen i.

Answer 1

standard form is a+bi where a and b are real numbers
remeber that i²=-1

ok


`(5)/(3-15i)`
we got to get the i out of the denomenator
remember the differnce of 2 perfect squares where (a-b)(a+b)=a²-b²

so multiply the whole thing by
`(3+15i)/(3+15i)`
we get

`(5(3+15i))/(3^2-(15i)^2)=(15+75i)/(9-225(-1))=(15+75i)/(9+225)=`
`(15+75i)/(234)=(15)/(234)+(75i)/(234)=(15)/(234)+(75)/(234)i=(5)/(78)+(25)/(78)i`

in standard form, it is
`(5)/(78)+(25)/(78)i`