Question

simplify the expression. write your answer as a complex number.

(2sqrt{25} + sqrt{-16})

• (10 + 4i)
• (10 - 4i)
• (10 + 8i)
• (10 - 8i)

question 4 (multiple choice worth 6 points)
(01.07r mc)

multiply ((6 - 7i)(3 - 6i)).

• (18 - 57i + 42i^2)
• (18 + 42i^2)
• (60 - 57i)
• (-24 - 57i)

Explanation:

Simplify the first expression

We simplify the real and imaginary parts of the expression \(2\sqrt{25} + \sqrt{-16}\).
First, evaluate the real square root:

$$2\sqrt{25} = 2 \cdot 5 = 10$$

Next, evaluate the imaginary square root using \(i = \sqrt{-1}\):

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

Combining these terms gives:

$$10 + 4i$$

Multiply the second expression

We expand the product of two complex numbers \((6 - 7i)(3 - 6i)\) using the FOIL method.
Multiply the terms:

$$(6)(3) + (6)(-6i) + (-7i)(3) + (-7i)(-6i)$$

$$= 18 - 36i - 21i + 42i^2$$

Simplify the product

Combine the imaginary terms and substitute \(i^2 = -1\):

$$18 - 57i + 42(-1)$$

$$= 18 - 57i - 42$$

Combine the real constants:

$$(18 - 42) - 57i = -24 - 57i$$

Answer:

Question 1

• (A) \(10 + 4i\) (Correct answer)
• (B) \(10 - 4i\)
• (C) \(10 + 8i\)
• (D) \(10 - 8i\)

Question 2

• (A) \(18 - 57i + 42i^2\)
• (B) \(18 + 42i^2\)
• (C) \(60 - 57i\)
• (D) \(-24 - 57i\) (Correct answer)