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

X = 3 + bi

|x| = √(3² + b²)

|x| = √(9 + b²) (a)

But from the question |x|² = 13

|x| = √13

Substitute this into equation (a)

|x| = √(9 + b²) (a)

√13 = √(9 + b²) 

13 = 9 + b²

9 + b² = 13

b² = 13 - 9

b² = 4

b = √4

b = + or - 2

Possible value of b is +2   or - 2.

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