Final answer:
The possible value of b in the complex number x = 3 + bı, given that |x| = 13, is found by solving the modulus equation. The nearest integer value to ±√160 is ±4, which makes option B) 4 the correct answer.
Step-by-step explanation:
To find the possible value of b in the complex number x = 3 + bı, where |x| = 13, we use the modulus of a complex number which is given by the square root of the sum of the squares of the real part and the imaginary part. In this case, the complex number x has a real part of 3 and an imaginary part of b.
Using the modulus formula, we get:
- |x| = √(3² + b²)
- 13 = √(9 + b²)
- 169 = 9 + b²
- b² = 160
- b = ±√160
- b = ±√(16×10)
- b = ±(4√10)
Since b must be an integer according to the given options, the closest value that is an integer and does not exceed the value obtained is b = 4 or b = -4. Among the provided options, the only one that is possible is option B) 4.