Using mathematically precise language, explain in detail how you would multiply the complex number z1=r1(cos theta1 + i sin thet

Question

dangina

26 days ago

6

Using mathematically precise language, explain in detail how you would multiply the complex number z1=r1(cos theta1 + i sin thet

a1) with the complex number z2=r2(cos theta2 + i sin theta2).

Mathematics

2 answers:

Inessa [9K] · Answer 1 · 2026-03-01T19:10:45+03:00

Answer:

Step-by-step explanation:

Given: The first complex number is $z_{1}=r_{1}(cos{\theta}_{1}+isin{\theta}_{1})$ and the second complex number is $z_{2}=r_{2}(cos{\theta}_{2}+isin{\theta}_{2})$

To find: The product of these two complex numbers.

Solution:

The first complex number is $z_{1}=r_{1}(cos{\theta}_{1}+isin{\theta}_{1})$ and the second one is $z_{2}=r_{2}(cos{\theta}_{2}+isin{\theta}_{2})$ . The formula for multiplying two complex numbers is as follows:

$z_{1}\times}z_{2}=(r_{1}(cos{\theta}_{1}+isin{\theta}_{1}){\times}r_{2}(cos{\theta}_{2}+isin{\theta}_{2}))$

$z_{1}z_{2}=r_{1}r_{2}(cos{\theta}_{1}+isin{\theta}_{1})(cos{\theta}_{2}+isin{\theta}_{2})$

$z_{1}z_{2}=r_{1}r_{2}(cos({\theta}_{1}+{\theta}_{2})+isin(({\theta}_{1}+{\theta}_{2}))$

which represents the desired product of the given complex numbers.

Svet_ta [9.5K] · Answer 2 · 2026-03-01T19:12:04+03:00

Svet_ta [9.5K]26 days ago

8 0

$r_1$ y $r_2$ representan, respectivamente, los módulos, mientras que $\theta_1$ y $\theta_2$ son, respectivamente, los argumentos de $z_1$ y $z_2$ .

El resultado de $z_1z_2$ se puede obtener multiplicando los módulos y sumando los argumentos, resultando en un número expresado como

$z_1z_2=r_1r_2(\cos(\theta_1+\theta_2)+i\sin(\theta_1+\theta_2))$