Question 70652
3+sqrt-25 divided by 4-sqrt-64
:
{{{(3+sqrt(-25))/(4-sqrt(-64))}}}
:
{{{(3+sqrt(25*-1))/(4-sqrt(64*-1))}}}
When have a sqrt of a negative, you must use "i" which is defined as the Sqrt(-1)
Find the square roots of 25 and 64 and -1 and you have:
:
{{{(3 + 5i)/(4 - 8i)}}}
:
They generally do not want "i" in the denominator so we multiply (4 - 8i) by it's
conjugate which is (4 + 8i); any number over itself is 1 so:
:
{{{(3 + 5i)/(4 - 8i)}}} = {{{(4 + 8i)/(4 + 8i)}}} = {{{(12 + 24i + 20i + 40i^2)/ (16 + 32i - 32i + 64i^2)}}} = {{{(12 + 44i + 40(-1))/ (16 - 64(-1))}}} = {{{(12 + 44i - 40)/(16 + 64))}}} = {{{(-28 + 44i)/80}}}
We can reduce the fraction (divide by 4) to {{{(-7 + 11i)/20}}}