we know that i=√-1
so we do pemdas
[tex] \frac{1}{2} i[/tex]=[tex] \frac{ \sqrt{-1} }{2} [/tex]
exponents
[tex]( \frac{ \sqrt{-1} }{2} )^{2}= \frac{( \sqrt{-1} )^{2}}{2^{2}} [/tex]=[tex] \frac{-1}{4} [/tex]
then [tex] (-2i)^{2} [/tex]=-2 times -2 times i times i=4 times -1=-4
now we have
[tex] 4i( \frac{-1}{4} )(-4) [/tex]=[tex]( \frac{-4i}{4} )(-4)[/tex]=[tex]( -i)(-4)[/tex]=4i=aprox 4√-1
the answer is 4i
