Final answer:
To find the complex number, use the provided components and equation to calculate the magnitude. Multiplying a complex number by its complex conjugate yields a real number, exemplified by the product of (3 + 4i) and its conjugate.
Step-by-step explanation:
The student has presented several concepts related to complex numbers and vector algebra. For finding the complex number, we use provided components (Cx, Cy, and C₂) and apply Equation 2.21, which results in the calculation of the magnitude of the complex number using the formula √(Cx² + Cy² + C₂²). This process is similar to finding the magnitude of a vector in three-dimensional space. Another key concept is the multiplication of a complex number a by its complex conjugate a*, which yields a real number as the result (a² + b²).
For the given example where a = 3 + 4i, the product a*a eliminates the imaginary part, resulting in a real number. This multiplication is described by the formula for finding the magnitude of a complex number a = a + ib, where the complex conjugate a* = a - ib. Multiplying a* by a, the imaginary parts cancel out, leaving us with a² + b² as the magnitude squared of the complex number.