Question

Simplify showing all steps: mula1" title="4i( \frac{1}{2}i)^2(-2i)^2" alt="4i( \frac{1}{2}i)^2(-2i)^2" align="absmiddle" class="latex-formula">

Answer 1

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