Show that for complex numbers z1 = r1(cosθ1 + isinθ1) and z2 = r2(cosθ2 + isinθ2), their product z1z2 = r1r2[cos(θ1 + θ2) + i sin(θ1 + θ2)].

Here's the solution to the questions from the image.

3b) Given the complex numbers $z_1 = r_1(\cos\theta_1 + i\sin\theta_1)$ and $z_2 = r_2(\cos\theta_2 + i\sin\theta_2)$, show that $z_1z_2 = r_1r_2[\cos(\theta_1 + \theta_2) + i\sin(\theta_1 + \theta_2)]$.

Step 1: Write the product $z_1z_2$.

$$$$