Question 420875
{{{(24(cos(150)+i*sin(150)))/(2(cos(30)+i*sin(30)))}}}
Dividing complex numbers written in polar form is fairly simple because there is a formula that makes it easy. For two complex numbers:
{{{z[1] = r[1](cos(x[1]) + i*sin(x[1]))}}}
and
{{{z[2] = r[2](cos(x[2]) + i*sin(x[2]))}}}
we can divide them using the formula:
{{{z[1]/z[2] = (r[1]/r[2])(cos(x[1]-x[2]) + i*sin(x[1]-x[2]))}}} (as long as {{{z[2]}}} is not zero).<br>
Using this formula to divide your complex numbers we get:
{{{(24/2)(cos(150-30) + i*sin(150-30))}}}
which simplifies to
{{{(12)(cos(120) + i*sin(120))}}}
which is the answer in polar form. For standard form, a+bi, we replace the cos and sin with their values. 120 is a special angle so we don't need a calculator:
{{{(12)((-1/2) + i*sqrt(3)/2)}}}
Distributing the 12 we get:
{{{-6 + i*(6sqrt(3))}}}
or
{{{-6 + (6sqrt(3))i}}}