Question 1133897

Can someone please help. Simplify the expression so that it is in the form (a + bi).
2/3-{ { {sqrt ( -1 ) } } } / { { { sqrt( -4 ) } } } + 1/2
<pre>{{{(2/3 - sqrt(- 1))/(sqrt(- 4) + 1/2)}}}
{{{(2/3 - i)/(2i + 1/2)}}} ------ Substituting {{{matrix(1,3, i, for, - 1)}}}
{{{((2 - 3i)/3)/((4i + 1)/2)}}} ======> {{{matrix(1,3, (2 - 3i)/3, "*", 2/(4i + 1))}}} =======> {{{2(2 - 3i)/3(1 + 4i)}}}
{{{2(2 - 3i)(1 - 4i)/3(1 + 4i)(1 - 4i)}}} ------ Multiplying numerator and denominator by the conjugate of 1 + 4i, or by 1 - 4i
{{{2(2 - 11i + 12i^2)/3(1 - 16i^2)}}}
{{{2(2 - 11i + 12(- 1))/3(1 - 16(- 1))}}} ------ Replacing {{{matrix(1,3, i^2, with, - 1)}}}
{{{2(2 - 11i - 12)/3(1 + 16)}}}
{{{2(- 10 - 11i)/3(17)}}}
{{{highlight_green(matrix(1,3, (- 20 - 22i)/51, "=", - 20/51 - (22/51)i))}}} <b><======== CORRECT ANSWER</b>