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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