Question

question 7 (5 points)
apply the square root principle to solve \\((x - 2)^2 + 20 = 0\\).
a) \\(x = -2 + 2\sqrt{5}, x = -2 - 2\sqrt{5}\\)
b) \\(x = 2 + 2i\sqrt{5}, x = 2 - 2i\sqrt{5}\\)
c) \\(x = -2 + 2i\sqrt{5}, x = -2 - 2i\sqrt{5}\\)
d) \\(x = 2 + 2\sqrt{5}, x = 2 - 2\sqrt{5}\\)

question 8 (5 points)
add the complex numbers: \\((4 + 8i) + (-2 - i)\\)
a) \\(6 + 7i\\)
b) \\(2 + 7i\\)
c) \\(2 + 9i\\)
d) \\(6 + 9i\\)

Explanation:

Isolate the squared term

Using the Square Root Principle knowledge point

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Apply the square root property

Using the Complex Quadratic Solutions knowledge point

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Group real and imaginary parts

To add the complex numbers \((4 + 8i) + (-2 - i)\), we group the real components together and the imaginary components together.

$$ \text{Real part: } 4 + (-2) = 2 $$

$$ \text{Imaginary part: } 8i + (-i) = 7i $$

Combine the components

Combining the real and imaginary parts gives the simplified complex number.

$$ (4 - 2) + (8 - 1)i = 2 + 7i $$

Answer:

Question 7

• A) \(x = -2 + 2\sqrt{5}\) , \(x = -2 - 2\sqrt{5}\)
• B) \(x = 2 + 2i\sqrt{5}\) , \(x = 2 - 2i\sqrt{5}\) (Correct answer)
• C) \(x = -2 + 2i\sqrt{5}\) , \(x = -2 - 2i\sqrt{5}\)
• D) \(x = 2 + 2\sqrt{5}\) , \(x = 2 - 2\sqrt{5}\)

Question 8

• A) \(6 + 7i\)
• B) \(2 + 7i\) (Correct answer)
• C) \(2 + 9i\)
• D) \(6 + 9i\)