Question 413608
I assume the i's are <i>not</i> inside the square roots. (If they are, then you might be able to figure the solution from the solution below anyway.)<br>
{{{(-1-sqrt(7)*i)(-1+sqrt(7)*i)}}}
You could use FOIL on this. But it will be faster if we recognize that this expression fits the pattern: {{{(a-b)(a+b) = a^2-b^2}}} with the "a" being -1 and the "b" being {{{sqrt(7)*i}}}. So from the pattern we know that the product will be {{{a^2-b^2}}}:
{{{(-1)^2 - (sqrt(7)*i)^2}}}
which simplifies as follows:
{{{1 - (sqrt(7))^2*i^2}}}
And since {{{(sqrt(7))^2 = 7}}} and {{{i^2 = -1}}} this becomes:
1 - (7)(-1)
which simplifies:
1 - (-7)
1 + 7
8
Note: If you use FOIL instead and use it correctly, you will still get 8 for the simplified answer.