Question

express \\(-2\sqrt{-16}\\) as a complex number (in terms of i):
\\-2\sqrt{-16} = \\

Explanation:

Identify the given expression

We are given the expression:

$$ -2\sqrt{-16} $$

Our goal is to express this as a complex number in terms of the imaginary unit \(i\).

Apply the definition of the imaginary unit

The imaginary unit \(i\) is defined as:

$$ i = \sqrt{-1} $$

We can rewrite the square root of a negative number using this definition:

$$ \sqrt{-16} = \sqrt{16 \cdot (-1)} = \sqrt{16} \cdot \sqrt{-1} $$

Simplify the square root

Calculate the square root of the positive real number \(16\):

$$ \sqrt{16} = 4 $$

Substitute this back to find the value of the radical:

$$ \sqrt{-16} = 4i $$

Multiply by the coefficient

Now, multiply this result by the coefficient \(-2\) from the original expression:

$$ -2\sqrt{-16} = -2 \cdot (4i) = -8i $$

Answer:

Express \(-2\sqrt{-16}\) as a complex number (in terms of i):
\(-2\sqrt{-16} =\) <blank>\(-8i\)</blank>