Question

How would you explain the multiplication problem solving in mathematically precise language? (Multiplication problem is in the image provided)

Answer 1

We need to find the product of z1 and z2, where

`\begin{gathered} z_1=r_1(\cos \theta_1+i\sin \theta_1) \\ z_2=r_2(\cos \theta_2+i\sin \theta_2) \end{gathered}`

At first, we will multiply r1 and r2

Then we will add Cita1 and Cita2

`z_1z_2=(r_1r_2)\lbrack\cos (\theta_1+\theta_2)+i\sin (\theta_1+\theta_2)\rbrack`

Then to multiply 2 complex numbers in the polar form

1. Multiply their magnitudes (r1, r2)

2. Add their angles (Cita1 and Cita2)