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Question 498435: I was wondering how to simplify the equation (-5-sqrt-3)^2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if i understand your equation, it is (-5-sqrt(-3))^2
(-5-sqrt(-3))^2 is equal to:
(-5-sqrt(-3)) * (-5-sqrt(-3)) which is equal to:
-5*(-5-sqrt(-3)) - sqrt(-3)*(-5-sqrt(-3))
this is because of the distributive property of algebra operations that states:
(a + b) * (c + d) is equal to a*(c + d) + b*(c + d)
multiplying out those terms gets:
25 + 5*sqrt(-3) + 5*sqrt(-3) + sqrt(-3)*sqrt(-3)
combine like terms and you get:
25 + 10*sqrt(-3) + (sqrt(-3))^2
simplify this further to get:
25 + 10*sqrt(-3) - 3
simplify this further to get:
22 + 10*sqrt(-3)
note that 22 + sqrt(-3) does not provide you with a real number.
the answer of 22 + 10*sqrt(-3) is a complex number.
it has a real part (22) and it has an imaginary part (10*sqrt(-3)).
never the less, (sqrt(-3))^2 does get you an answer of -3.
this is because when you square the square of a number, you get the number.
example:
(sqrt(4))^2 = 4 (sqrt(4) = 2 and 2^2 = 4)
back to your complex number....
22 + 10*sqrt(-3) is a complex number.
it can be simplified further as follows:
sqrt(-3) = sqrt(3)*i, where i is equal to sqrt(-1)
your answer can therefore be shown as:
22 + 10*sqrt(3)*i
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