## Complex Numbers: Write each espression in the form a +bi where a and b are real numbers: (8 +sqrt -20)/-4?

**Answer**

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 )

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