The length of the vector that could correctly be used to represent in the complex plane the number \( 3-i \sqrt{2} \) is (A) 11 (B) \( \sqrt{11} \) (C) \( 3 \sqrt{2} \) (D) \( \sqrt{5} \) (E) \( \sqrt{13} \)

To find the length (or modulus) of the complex number \( 3 - i \sqrt{2} \), we use the formula \( |z| = \sqrt{x^2 + y^2} \), where \( z = x + yi \). Here, \( x = 3 \) and \( y = -\sqrt{2} \): \[ |z| = \sqrt{3^2 + (-\sqrt{2})^2} = \sqrt{9 + 2} = \sqrt{11}. \] Therefore, the correct answer is (B) \( \sqrt{11} \). Did you know that the length of a complex number can represent its distance from the origin in the complex plane? Just like a point on a map can be described using coordinates, a complex number does the same in a two-dimensional space! If you ever need to work with complex numbers, it's helpful to remember that they can be added and multiplied, just like vectors. This opens up a whole world of applications in fields like electrical engineering and fluid dynamics, where complex numbers simplify calculations significantly!