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

• jisbon
In summary: Yes, the RHS is a non-negative real number. What does that say about ##z##? Hint: start with ##z=a+bi##
jisbon said:
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.

PeroK said:
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

jisbon said:
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 said:
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.
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.

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