write each espression in the form a +bi where a and b are real numbers: 8 +sqrt -20/-4?

Question

this is an algebra question. 8 +sqrt of -20 divided by -4.

Answer 1

√(-20/-4) = √(5)

so 8+√(-20/-4) = 8+√(5)
There is no imaginary part so b = 0 and a = 8+√(5)

The answer is (8+√(5)) + 0i

Answer 2

8 +sqrt of -20 divided by -4.

sqrt ( -1 ) = i

[ 8 +sqrt of -20 ] / - 4
= ( 8 / {- 4} ) + ( sqrt ( -20) /{ - 4} )
= - 2 - 4 sqrt ( -20 )
= - 2 - 4 sqrt ( - 1* 5 * 4 )
= - 2 - 4 *sqrt(-1)*sqrt(5)*sqrt(4)
= - 2 - 4* i* sqrt(5)*2
= - 2 - 8*sqrt(5)*i
= - 2 - 8sqrt(5) i
which is in the form a + bi with
a = - 2 and b = - 8 sqrt ( 5 )

Hope this helped

:)