\( z_{1}=3 \) cis \( 25^{\circ} \) and \( z_{2}=2,9 \) cis \( 65^{\circ} \) are two complex numbers. 2.2.1 \( \quad \) Calculate \( \left(z_{1}\right)\left(z_{2}\right) \). Leave your answer in polar form. 2.2.2 \( \quad \) Calculate \( z_{1}+z_{2} \)

To calculate \( z_{1} z_{2} \): First, we multiply the magnitudes: \[ |z_{1}| \cdot |z_{2}| = 3 \cdot 2.9 = 8.7. \] Next, we add the angles: \[ 25^{\circ} + 65^{\circ} = 90^{\circ}. \] Thus, \[ z_{1} z_{2} = 8.7 \text{ cis } 90^{\circ}. \] Now, onto \( z_{1} + z_{2} \): Convert both complex numbers to rectangular form: \[ z_{1} = 3 (\cos 25^{\circ} + i \sin 25^{\circ}) = 3 \left(0.9063 + 0.4226i\right) \approx 2.7189 + 1.2678i, \] \[ z_{2} = 2.9 (\cos 65^{\circ} + i \sin 65^{\circ}) = 2.9 \left(0.4226 + 0.9063i\right) \approx 1.2235 + 2.6273i. \] Now, add them: \[ z_{1} + z_{2} \approx (2.7189 + 1.2235) + (1.2678 + 2.6273)i \approx 3.9424 + 3.8951i. \] So, \( z_{1} + z_{2} \approx 3.9424 + 3.8951i \).