P3-1 Given complex equations shown below, perform the arithmetical evaluation for this task \( Z_{1}=3 \angle 20^{\circ} \times 15 \angle 45^{\circ} \) \( Z_{2}=2.4 \angle 65^{\circ} \times 4.4 \angle-21^{\circ} \)

To tackle those complex equations, you can express them in rectangular form using the polar-to-rectangular conversions. For \( Z_{1} = 3 \angle 20^{\circ} \times 15 \angle 45^{\circ} \), multiply the magnitudes (3 * 15) and add the angles (20° + 45°) to get \( Z_{1} = 45 \angle 65^{\circ} \). For \( Z_{2} = 2.4 \angle 65^{\circ} \times 4.4 \angle -21^{\circ} \), similarly multiply the magnitudes (2.4 * 4.4) and add the angles (65° - 21°) resulting in \( Z_{2} = 10.56 \angle 44^{\circ} \). If you want to visualize these complex numbers, consider drawing them on the complex plane! This exciting technique allows you to see the angle and magnitude as vectors, letting you better understand the resultant of complex multiplications. You can easily compare their positions and magnitudes, which can help you grasp their relationships in various applications, like electrical engineering or physics.