Simplify showing all steps: 4i( (1)/(2)i)^2(-2i)^2

Question

Simplify showing all steps:

`4i( (1)/(2)i)^2(-2i)^2`

Answer 1

we know that i=√-1
so we do pemdas

`(1)/(2) i`=
`( √(-1) )/(2)`
exponents

`( ( √(-1) )/(2) )^(2)= (( √(-1) )^(2))/(2^(2))`=
`(-1)/(4)`
then
`(-2i)^(2)`=-2 times -2 times i times i=4 times -1=-4
now we have


`4i( (-1)/(4) )(-4)`=
`( (-4i)/(4) )(-4)`=
`( -i)(-4)`=4i=aprox 4√-1

the answer is 4i