X = 3ej0.2π + 8ej0.8π

Question

Determine the imaginary portion of the complex number, X.

X = 3ej0.2π + 8ej0.8π

Answer 1

These expressions are in polar form. Each must be individually converted to rectangular form. Then the imaginary parts can be summed.

X = 3ej0.2π + 8ej0.8π = 3<0.2pi + 8<0.8pi

= 3cos(0.2pi) + j3sin(0.2pi) + 8cos(0.8pi) + j8sin(0.8pi)

= 3(0.81) + j3(0.59) + 8(-0.81) + j8(0.59)

Im[X] = 3(0.59) + 8(0.59) = 6.5