- #1

Magnetons

- 18

- 4

- Homework Statement
- compute ##z^n+ \frac 1 z^n##

if ##z+\frac 1 z= \sqrt3##

- Relevant Equations
- No Equation

Firstly I converted the given equation to a quadratic equation which is

##z^2- (\sqrt3)z+1=0##

I got two solutions:

1st sol ##z=\frac {(\sqrt3 + i)} {2}##

2nd sol ## z=\frac {(\sqrt3 -1)} {2}##

Then I found modulus and argument for both solution . Modulus=1 Arguments are ##\frac {\Pi} {6}## and ##\frac {11* \Pi } {6}##

My question is {Why we consider only one argument ##\frac {\Pi} {6}## and not other}

##z^2- (\sqrt3)z+1=0##

I got two solutions:

1st sol ##z=\frac {(\sqrt3 + i)} {2}##

2nd sol ## z=\frac {(\sqrt3 -1)} {2}##

Then I found modulus and argument for both solution . Modulus=1 Arguments are ##\frac {\Pi} {6}## and ##\frac {11* \Pi } {6}##

My question is {Why we consider only one argument ##\frac {\Pi} {6}## and not other}

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