Answer: (-2i+ √5)(-21-√-5) simplifies to -19√5 + 42i - 5.
Explanation:
To simplify the expression (-2i+ √5)(-21-√-5), we can first use the distributive property to expand the product:
(-2i)(-21) + (-2i)(-√-5) + (√5)(-21) + (√5)(-√-5)
Simplifying each term, we get:
42i + 2i√-5 - 21√5 - √25
Note that √-5 can be written as √(-1)√5 = i√5, using the fact that √-1 = i. Also, √25 = 5, so we can substitute these values to get:
42i + 2i√5 - 21√5 - 5
Combining like terms, we have:
(2i√5 - 21√5) + (42i - 5)
-19√5 + 42i - 5