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 = 3² + b²

Substituting the value of |x|²

13 = 9 + b²

By further calculation

b² = 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.