# How do you simplify # (sqrt(-4)+3)(2sqrt(-9)-1)#?

Substituting this into the original expression, we get:

Now, distribute using the FOIL method.

By signing up, you agree to our Terms of Service and Privacy Policy

To simplify the expression ((\sqrt{-4}+3)(2\sqrt{-9}-1)), we first simplify the square roots:

(\sqrt{-4} = 2i) and (\sqrt{-9} = 3i).

Now, we substitute these values back into the expression and perform the multiplication:

((2i + 3)(2 \cdot 3i - 1))

(= (2i + 3)(6i - 1))

Next, we distribute:

(= 2i \cdot 6i - 2i \cdot 1 + 3 \cdot 6i - 3)

(= 12i^2 - 2i + 18i - 3)

Since (i^2 = -1), we have:

(= 12(-1) - 2i + 18i - 3)

(= -12 - 2i + 18i - 3)

Now, combine like terms:

(= -12 + 16i - 3)

(= -15 + 16i)

So, ((\sqrt{-4}+3)(2\sqrt{-9}-1)) simplifies to (-15 + 16i).

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7