Question E5C02:
How are impedances described in polar coordinates?  

Choices:  
A: By X and R values  
B: By real and imaginary parts  
C: By magnitude and phase angle  
D: By Y and G values    

Correct Answer is  C: By magnitude and phase angle  

Correct answer: C — By magnitude and phase angle.

Why it’s correct:
- In polar form, impedance is written as $Z = |Z|\angle \theta$, where:
  - $|Z|$ is the magnitude in ohms,
  - $\theta$ is the phase angle (degrees or radians), indicating the phase of the reactive part relative to the resistive axis.

Why the others are incorrect:
- A: “By X and R values” — That’s rectangular (Cartesian) form: $Z = R + jX$, not polar.
- B: “By real and imaginary parts” — Also rectangular form: real part $R$, imaginary part $X$.
- D: “By Y and G values” — $Y$ is admittance (the reciprocal of impedance), and $G$ is conductance (the real part of $Y$). This does not describe impedance, and it’s not polar.

Useful formulas:
- Rectangular to polar:
  $$|Z| = \sqrt{R^2 + X^2}$$
  $$\theta = \tan^{-1}\!\left(\frac{X}{R}\right)\quad \text{(use atan2 for correct quadrant)}$$
- Polar to rectangular:
  $$R = |Z|\cos\theta$$
  $$X = |Z|\sin\theta$$

Rules of thumb:
- $X > 0$ (positive) → inductive; $X < 0$ (negative) → capacitive.
- Pure resistance has $\theta = 0^\circ$; pure reactance has $R = 0$ and $\theta = \pm 90^\circ$.