Perform the indicated operation(s) and express the result in standard form. Leave answers in terms of square roots (do not use decimals).
(-9-sqrt-3)^2
[-9 -sqrt(-3)]^2
let me change that to i notation (i=sqrt-1)
[-9- i sqrt3]^2
Using FOIL
81+9isqsrt3 +9isqrt3+i^2*3
81+18i*sqrt3 -3
78+18i*sqrt3
remember i^2=-1
To perform the indicated operation, we first need to simplify the expression inside the parentheses, and then square the result.
The expression inside the parentheses is (-9 - sqrt(-3)). We notice that the term sqrt(-3) represents an imaginary number since the square root of a negative number is not a real number.
To simplify sqrt(-3), we can use the imaginary unit i, where i = sqrt(-1). Therefore, sqrt(-3) can be written as sqrt(3) * i.
Now, we can rewrite the expression inside the parentheses as (-9 - sqrt(3) * i).
To square this expression, we use the formula (a-b)^2 = a^2 - 2ab + b^2.
Applying this formula, we get:
(-9 - sqrt(3) * i)^2 = (-9)^2 - 2*(-9)*(sqrt(3)*i) + (sqrt(3)*i)^2
= 81 - 2*(-9)*(sqrt(3)*i) + 3*(-1)
= 81 + 18(sqrt(3)*i) - 3
Now, let's simplify the expression further:
81 + 18(sqrt(3)*i) - 3 = 78 + 18(sqrt(3)*i)
Therefore, (-9 - sqrt(-3))^2 simplifies to 78 + 18(sqrt(3)*i) in standard form.