\( z_{1}=3 \) 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 \( z_{1}+z_{2} \)

We are given:   z₁ = 3 cis 25°  and  z₂ = 2.9 cis 65°. Step 1. Multiply z₁ and z₂ in polar form. When multiplying complex numbers in polar form, we multiply the moduli and add the angles:   z₁ · z₂ = (3 × 2.9) cis (25° + 65°)       = 8.7 cis 90°. So, the answer to 2.2.1 is:   z₁z₂ = 8.7 cis 90°. Step 2. Add z₁ and z₂. To add in rectangular form, convert each number:   z₁ = 3 (cos 25° + i sin 25°)   z₂ = 2.9 (cos 65° + i sin 65°). Using approximate trigonometric values:   cos 25° ≈ 0.9063 and sin 25° ≈ 0.4226,   cos 65° ≈ 0.4226 and sin 65° ≈ 0.9063. Now compute:   z₁ ≈ 3 (0.9063 + i·0.4226) = 2.7189 + 1.2678i,   z₂ ≈ 2.9 (0.4226 + i·0.9063) = 1.2255 + 2.6273i. Adding the real parts and the imaginary parts:   Real part = 2.7189 + 1.2255 = 3.9444,   Imaginary part = 1.2678 + 2.6273 = 3.8951. Thus, in rectangular form:   z₁ + z₂ ≈ 3.9444 + 3.8951i. (Optional) To express this sum in polar form, compute the modulus r and the angle θ: 1. Modulus r:   r = √(3.9444² + 3.8951²)    ≈ √(15.556 + 15.172)    ≈ √30.728    ≈ 5.54. 2. Angle θ:   θ = arctan(3.8951 / 3.9444)    ≈ arctan(0.9874)    ≈ 44.6°. So in polar form:   z₁ + z₂ ≈ 5.54 cis 44.6°. Thus, the answers are: 2.2.1: z₁z₂ = 8.7 cis 90°. 2.2.2: z₁ + z₂ = 3.9444 + 3.8951i  (or equivalently, ≈ 5.54 cis 44.6°).