Question 250429
{{{(4+9i)/12i}}}
Since a + bi has two terms, we will start by splitting this fraction into two terms:
{{{4/12i+9i/12i}}}
(Think of the above as "un-adding".) Next we can simplify the fractions:
{{{1/3i+3/4}}}
Since i = {{{sqrt(-1)}}} we do not want it in the denominator. We can rationalize the first fraction by multiplying the top and bottom by i:
{{{(1/3i)(i/i)+3/4}}}
{{{i/3i^2 + 3/4}}}
Since {{{i^2 = -1}}}:
{{{i/3(-1) + 3/4}}}
{{{i/(-3) + 3/4}}}
We want the real term, a, in front:
{{{3/4 + i/(-3)}}}
We want b*i not i divided by something so, since dividing by -3 is the same as multiplying by -1/3:
{{{3/4 + ((-1)/3)i}}}