If the complex number x = 3 + bi and |x|^2 = 13, which is a possible value of b?

a. 2

b. 4

c. 9

d. 10

The correct answer is:

A) 2.

Explanation:

We know that |x|² = 13 and x = 3+bi:

(3+bi) ² = 13

3² + b² = 13

9 + b² = 13

Subtract 9 from each side:

9 + b² - 9 = 13 - 9

b² = 4

Take the square root of each side:

√b² = √4

b = 2

The question is asking to choose among the following choices that states the possible value of b if the complex number x = 3+bi and |x|^2 = 13, base on that the answer would be a. 2. I hope you are satisfied with my answer and feel free to ask for more if you have questions and further clarifications