contestada

Consider the number z = 5 – 5i StartRoot 3 EndRoot. What happens when z is raised to successively increasing powers?
Use the drop down menus to complete each sentence.
The modulus increases by a factor of
The argument increases by
Pi over 3.

Consider the number z 5 5i StartRoot 3 EndRoot What happens when z is raised to successively increasing powers Use the drop down menus to complete each sentence class=

Respuesta :

Answer:

10 & 5

Step-by-step explanation:

I just did the assignment EDG2021

varshamittal029

The modulus increases by a factor of 10 and the argument increases by 5π/3.

What is the modulus of the complex number?

The modulus of the complex number is the magnitude of the complex number. If z is the complex number such that z= p+qi

Then the modulus of the z will be =|z|= √p²+q²

We have,

z = 5 – 5i √3

So,

Now rewrite this given equation in the form of z = r(CosΘ + iSinΘ),

For this first calculate the modulus,

|Z| = √((5√3)² + 5²)

|Z| = √(25×3 + 25)

|Z| = √(100) = 10

And,

Argument, Θ = tan⁻¹ (b/a)

Θ = tan⁻¹ (5√3/5)

Θ = tan⁻¹ (√3)

Θ = 71

Therefore, the modulus increases by a factor of 10, and the argument increase by 5π/3.

Learn more about the modulus and argument here:

https://brainly.com/question/2288736

#SPJ2

Otras preguntas