Final answer:
To simplify the complex-valued sum and find the numerical answer in polar form, add the real parts and the imaginary parts separately by using the formulas for cosine and sine of a sum. To draw the vector diagram, represent each complex number as a vector with magnitude and angle.
Step-by-step explanation:
To simplify the complex-valued sum z = ej9π/3 + e−j5π/8 + ej13π/8, we can add the real parts and the imaginary parts separately. The real part of z can be found by adding the cosines, and the imaginary part of z can be found by adding the sines. In polar form, the magnitude of z is the absolute value of the complex number, and the angle is the argument of the complex number. By using the formulas for cosine and sine of a sum, we can simplify the expression and find the numerical answer for z in polar form. To draw the vector diagram, we can represent each complex number as a vector, with the magnitude and the angle. The sum of the vectors will be the vector representation of z.