Question

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

a) 2
b) 4
c) 9
d) 10

Answer 1

The complex number x = 3 + bi has a magnitude squared of 13. To find b, we set up the equation 9 + b^2 = 13 and solve for b, resulting in b = ±2. The positive possible value for b is 2.

Step-by-step explanation:

The magnitude squared of the complex number x = 3 + bi is given as |x|² = 13. To find the value of b, we use the formula for the magnitude of a complex number which is √(a² + b²), where a and b are the real and imaginary parts of the complex number respectively. Squaring both sides of the magnitude we get a² + b² = |x|². Substituting the values we have:

3² + b² = 13

9 + b² = 13

b² = 13 - 9

b² = 4

Therefore, when we take the square root of both sides to solve for b, we find that:

b = ±√4

b = ±2

Since b can be positive or negative, but we're looking for a possible positive value of b, the answer is b = 2.