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

We can make use of the modular properties of the complex number.

Answer: If the complex number x = 3 + bi and |x|² = 13, the possible value of b is 2 or -2.

Go through the steps to understand better.

Explanation:

Given:  x = 3 + bi,  |x|² = 13

⇒  |x|² = 13

Using the definition of modular of a complex number, we get:

|x|² = 3² + b²

13 = 9 + b²

13 - 9 = b²

b² = 4

b = 2, -2

Therefore, the value of b is calculated to be 2 or -2.