Okay, I have the first step, but after that, they ask me to expand and I'm not sure where they're getting the next numbers from.
Original question:
(-3- sqrt(-7))^2
Now, my first step should be:
(-3-i sqrt(7))^2
After that, I'm lost. I see what they're doing after that, but I don't know where the numbers are coming from or how to recreate the answer.
Help, please. :)
Thank you!
(A+B)^2=A^2+2AB+B^2
sqrt(A)^2=A
(-A)^2 = A^2
See if you can get further with these hints.
I still don't see where it's coming from. I'm sorry. :)
(-3-i√7)^2
= 9 + 6i√7 + i^2(7) , but i^2 = -1
= 9 + (6√7)i - 7
= 2 + (6√7)i
Notice I followed exactly the steps that MathMate had outlined for you.
To expand the expression (-3 - √(-7))^2, you first need to square the binomial expression (-3 - √(-7)). To do so, you can use the FOIL method, which stands for First, Outside, Inside, Last.
First, multiply the first terms of each binomial: (-3) * (-3) = 9.
Outside, multiply the outer terms: (-3) * (√(-7)) = -3√(-7).
Inside, multiply the inner terms: (√(-7)) * (-3) = -3√(-7).
Last, multiply the last terms of each binomial: (√(-7)) * (√(-7)) = (√(49)) = 7.
Adding all the resulting terms together, you get:
9 + (-3√(-7)) + (-3√(-7)) + 7
Simplifying further, you can combine like terms:
9 - 6√(-7) + 7
Finally, combining the constants:
16 - 6√(-7)
Therefore, the expanded form of (-3 - √(-7))^2 is 16 - 6√(-7).