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