The sq root of -4 (3-sq root of -9)
a)6 +6i
b)-6+6i
c)6-6i
d)-6-6i
Again the i's are in italics. I would think that c and d could be eliminated because the answer is suppose to be in the form a + bi but they could be trting to trick you.
I'm not quite sure what your problem is, so I'm going to assume it's something like the following:
√-4(3 - √-9)
i = √-1
i^2 = -1
Note: I'm using ^2 to mean squared.
√-4 = 2i
√-9 = 3i
Now we have: 2i(3 - 3i)
Simplifying:
6i - 6i^2 =
6i - 6(-1) =
6i + 6
..or..
6 + 6i
I hope this helps and is what you were asking.
To evaluate the given expression √-4(3 - √-9), we can break it down step by step:
1. Simplify the square roots:
Since i is defined as √-1, we have:
√-4 = √(4 * -1) = √4 * √-1 = 2i
Similarly,
√-9 = √(9 * -1) = √9 * √-1 = 3i
2. Substitute the simplified square roots into the expression:
√-4(3 - √-9) = 2i * (3 - 3i)
3. Distribute the multiplication:
2i * 3 - 2i * 3i = 6i - 6i^2
4. Simplify i^2:
Since i^2 = -1, we substitute:
6i - 6(-1) = 6i + 6 = 6 + 6i
Therefore, the correct answer is option a) 6 + 6i.