Question

perform the indicated operations & simplify.

add: \\((25 - \sqrt{-64}) + (-7 + \sqrt{-16})\\)
sum =

subtract: \\((25 - \sqrt{-64}) - (-7 + \sqrt{-16})\\)
difference =

Explanation:

Simplify the radical terms

Using the Imaginary Unit and Simplifying Radicals knowledge points, we rewrite the square roots of negative numbers:

$$ \sqrt{-64} = \sqrt{64} \cdot \sqrt{-1} = 8i $$

$$ \sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i $$

Rewrite the complex numbers

Using the Complex Numbers knowledge point, we substitute the simplified radical values back into the expressions:

$$ 25 - \sqrt{-64} = 25 - 8i $$

$$ -7 + \sqrt{-16} = -7 + 4i $$

Calculate the sum

We add the real parts and the imaginary parts:

$$
LATEXBLOCK0
$$

Calculate the difference

We subtract the real parts and the imaginary parts:

$$
LATEXBLOCK1
$$

Answer:

Question 1

sum = \(18 - 4i\)

Question 2

difference = \(32 - 12i\)