Complex number equation and roots of unity

[math_nuub]

I have some math problems

What is the solution to this equation :

z dash(complex conjugate) = z^3 Z is complex number

I try to multiply both sides by Z in the left i get Z dash Z => |Z| but i don't see the solution

----

P is primitive 9th root of unity.
Calculate the sum 1 + 2P +3P^2 + ... + 9P^8


---
Thx.

 

[haruspex]

The easiest approach is using polar notation.
Alternatively, consider the magnitude of z. Notice anything?
And you already got |z|² = z⁴, right? What interesting fact does that tell you about the complex number z⁴?

 

[math_nuub]

I don't know what is the interesting fact behind Z^4?

 

[haruspex]

I don't know what is the interesting fact behind Z^4?

It's a complex number, and yet it equals |z|², so in fact ... ?

 

[SammyS]

I have some math problems

What is the solution to this equation :

z dash(complex conjugate) = z^3 Z is complex number

I try to multiply both sides by Z in the left i get Z dash Z => |Z| but i don't see the solution
----
P is primitive 9th root of unity.
Calculate the sum 1 + 2P +3P^2 + ... + 9P^8
---
Thx.

Hello math_nuub. Welcome to PF !

According to the rules for Homework Help on this Forum, you need to show some effort before we can help.

What have you tried?

Where are you stuck?

 

[math_nuub]

I am really trying to understand but my test is approaching and i could.t wrap my head around this material

It's a complex number, and yet it equals |z|2, so in fact ... ?

|Z|^2 is a Real number so you mean that |z|^4 is Real number also?

What have you tried?

Where are you stuck?

I am trying from two days to understand those rots of unity.

I don't understand whiht is the 9th primitive root of unity. I think there are several of them (1,2,4,5,7,8), but how could i sum them, There are in trigonometric form.

 

[SammyS]

I am really trying to understand but my test is approaching and i could't wrap my head around this material

|Z|^2 is a Real number so you mean that |z|^4 is Real number also?

Of course |z|⁴ is a real number.

It means that z⁴ is a real number.

I am trying from two days to understand those rots of unity.

I don't understand what is the 9th primitive root of unity. I think there are several of them (1,2,4,5,7,8), but how could i sum them, There are in trigonometric form.

What is the definition of a "primitive root of unity" ?