# If the complex number x = 3 + bi and |x|^{2} = 13, which is a possible value of b? 2, 4, 9, 10

**Solution:**

x = 3 + bi and |x|^{2} = 13 (Given)

The sum of a real number and an imaginary number is called a complex number.

From the definition of modular of a complex number

|x|^{2} = 3^{2} + b^{2}

Substituting the value of |x|^{2}

13 = 9 + b^{2}

By further calculation

b^{2} = 13 - 9 = 4

So we get,

b = 2, -2

Therefore, the possible value of b is 2 or -2.

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

**Summary:**

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