Complex numbers simplification

1. Jan 24, 2016

Mrencko

• Member warned about posting unclear question with missing information
1. The problem statement, all variables and given/known data
Z=((2z1)+(4z2))/(z1)(z2) where Z1=4e^2pi/3
Z2=2/60 degre, z3=1+i
The answer must be in polar form r/theta

2. Relevant equations
Well in the upper section

3. The attempt at a solution
After do some operations i get to this and unable to convert to polar form... - i((squarert3+1)/2) i need some help, the polar form go to infinite when i apply arctan(y/x)

Last edited by a moderator: Jan 24, 2016
2. Jan 24, 2016

Dr. Courtney

I don't see a question.

3. Jan 24, 2016

Mrencko

The thread implies, the "question" or in this case an issue whit the problem stated at the start, so i need to convert my answer to polar form but i cant because one C/0 so i need to know if i have a good answer and its not possible to convert to polar or if i did some mistake in operating the complex numbers

4. Jan 24, 2016

SammyS

Staff Emeritus
We should not have to guess what your question is. A complete statement of the problem should be given in the body of the post which initiates the thread, no matter what is the thread's title.

I addition to that, It looks as if you have some typographical errors in the statement of your problem.

What do you mean by " Z2=2/60 degre, " ?

What is z3 to be used for?

5. Jan 24, 2016

Mrencko

Oh sorry you are right z3 its for (2z1+4z3)/z1z2, and z2 its in the polar form
Where 2=r and 60=theta

6. Jan 24, 2016

SammyS

Staff Emeritus
z1 looks like it was written in a form close to being in polar form except that there is an i (imaginary unit) missing from the exponent.

Is it intended that $\displaystyle \ z_1=4e^{2\pi i/3} \$ ?

7. Jan 24, 2016

Mrencko

yes sorry again i assume the imaginary unit will be implicit in the exponential form of complex numbers, well doing my research, appears to be correct and the polar form will be: in the form Rθ being theta= -90 so tell me if i am correct, or incorrect please, just to finish properly my homework :)

8. Jan 24, 2016

Staff: Mentor

No, that's not true. $e^{2\pi/3}$ is a real number, and $e^{2i\pi/3}$ is a complex number.

9. Jan 24, 2016

Mrencko

Sorry for that

10. Jan 24, 2016

SammyS

Staff Emeritus
Is that $\displaystyle \ -i\frac{\sqrt{3}+1}{2}\$, or something else? (You have been a bit careless with parentheses.)

For what values of θ, is tan(θ) undefined (sort of like being infinite)?

11. Jan 24, 2016

Mrencko

Yes that its my finale answer, and for the indetermination of theta i use the form thetha=arctan(y/x) so if my answer its pure complex number, so y/0 its infinite right? For r the value exist for thetha doesn't exist

12. Jan 24, 2016

Mrencko

Being x the real part and y the complex in the form x+yi

13. Jan 24, 2016

SammyS

Staff Emeritus
How do you convert polar form, let's say 2/60°, to the form, x + yi ?

14. Jan 24, 2016

Mrencko

Whit the form x=rcosthetha y=rsinthetha
To the form x+yi

15. Jan 24, 2016

SammyS

Staff Emeritus
Fine.

So what does θ need to be to get x = 0 and get y to be negative (actually -r) ?

16. Jan 24, 2016

Mrencko

It must be in 90 degres to get rcos90=0, but i dont get the think of - r

17. Jan 24, 2016

SammyS

Staff Emeritus
Well sin(90°) = 1 , so 90° won't do what's needed.

What does θ need to be for sin(θ) = -1 ? What is cosine for this θ ?

18. Jan 24, 2016

Mrencko

I guess - 90 degrees to get the both answers

19. Jan 24, 2016

SammyS

Staff Emeritus
Correct.

Does that work out for the problem you're working on in this thread?

20. Jan 24, 2016

Mrencko

Yes then i must say the polar form of my complex number its given by R=√((√3+1)/2)^2 and thetha=-90 degres by definition