Question

simplify 4+2i over 2/3+1/2i

Answer 1

if it was me i would multiply top and bottom by 6 first because i hate compound fractions. that would give you
\[\frac{24+12i}{2+3i}\]
multiply numerator and denominator by the "conjugate" of the denominator. the conjugate of
\[a+bi\] is
\[a-bi\] and it is always true that
\[(a+bi)(a-bi)=a^2+b^2\] a real number. so in your case you will get
\[\frac{(24+12i)(2-3i)}{2^2+3^2}\] and go from there