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

How Would You Explain The Multiplication Problem Solving In Mathematically Precise Language Multiplication Problem Is In The Image Provided class=

Answer :

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

[tex]\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}[/tex]

At first, we will multiply r1 and r2

Then we will add Cita1 and Cita2

[tex]z_1z_2=(r_1r_2)\lbrack\cos (\theta_1+\theta_2)+i\sin (\theta_1+\theta_2)\rbrack[/tex]

Then to multiply 2 complex numbers in the polar form

1. Multiply their magnitudes (r1, r2)

2. Add their angles (Cita1 and Cita2)