# 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: The value of b is calculated to be sqrt(133/4).

Go through the steps to understand better.

**Explanation:**

Given: x = 3 + bi, |x|2 = 13

⇒ |x| = 13/2

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

|x| = sqrt(3^{2} + b^{2})

|x| = sqrt(9 + b^{2})

13/2 = sqrt(9 + b^{2})

On squaring, on both the sides.

⇒ 169/4 = 9 + b^{2}

⇒ b = sqrt(133/4)