How Do You Solve Complex Number Equations in Quadratics and Exponentials?

[PeroK]

Oh okay. So by proving b=0, we can now assume z = 4/7 +0i right?
Also for the next question, I've edited to include my initial answers. Do you think they are correct? Thanks.

I think I'd post the remaining questions in a new thread.

 

[jisbon]

I think I'd post the remaining questions in a new thread.

I could post them. Oh and for the previous question, it will be z=4/7+0i right? Thanks

 

[PeroK]

I could post them. Oh and for the previous question, it will be z=4/7+0i right? Thanks

You should be able to check that for yourself. Once you know that $z$ is real, it's a fairly simple question.

 

[jisbon]

You should be able to check that for yourself. Once you know that $z$ is real, it's a fairly simple question.

Yep checked it's correct.
Here's the new link: https://www.physicsforums.com/threads/help-with-complex-numbers-2.976744/
Attempted 2 of them, I really do not know how to proceed with the last question unfortunately

 

[scottdave]

Homework Statement: NIL
Homework Equations: NIL

Hello all!
Thanks for helping me out so far :) Really appreciate it.
I don't seem to understand some of the questions presented to me, so if anyone has an idea on how to start the questions, please do render your assistance :)
7)
Let
$\sum_{k=0}^9 x^k = 0$
Find smallest positive argument. Same thing as previous question, but I guess I can expand to
z+z2+z3+...+z9=0z+z2+z3+...+z9=0
$z=re^iθ$
$rei^θ+re^2iθ+re^3iθ+...$
What do I do to proceed on?
Cheers

This would be easier if you ask only 1 (or 2 max, if they are pretty simple) questions at a time.
On your summation, you start with x^k then switch to x^k when you expand it out.
Also in the sum, it's k = 0 to 9, so what happened to the zero power? $z^0 = 1$
If $z=re^{iθ}$ then shouldn't $z^2 = (re^{iθ})^2 = r^2e^{i2θ}$

Latex tip: use curly braces { } to put multiple characters in the exponent.