Principal value of an argument

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The discussion revolves around the challenge of determining the principal value of an argument in a mathematical context. The user attempts to derive inequalities involving n and θ but struggles with the relevance of their final answer, which includes two unknowns. Feedback highlights that the inequalities presented are flawed and that the assumptions made do not hold for all cases. A suggestion is made to simplify the problem by assuming a specific value for θ, such as π/4, to clarify the solution. The conversation emphasizes the importance of correctly applying definitions and assumptions in mathematical arguments.
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Homework Statement
Let 0<θ<π/2 . The principal value corresponding to the argument 11π+θ is
(a) θ+π
(b) θ-π
(c) π-θ
(d) -θ-π
Relevant Equations
argz = Argz +2πn n=0,±1,±2...
This is my attempt of the problem

Argz = (11π+θ) - 2πn
0 < (11π+θ) - 2πn < π/2
0 < (11π+θ) - 2πn or (11π+θ) - 2πn < π/2
n < (11π+θ)/2π or n > (21π/4 + θ)

(21π/4 + θ) < n < (11π+θ)/2π, what i was trying to do was to find the value of n which i thought would help me obtain the value of the Argument 'Arg' of z but unfortunately I'm nowhere near getting the correct answer because my final answer has two unknowns which I think aren't even relevant to getting the correct answer, please assist
 
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All your inequalities are bad. You don't know if ##0< 11\pi + \theta -2\pi n < \pi/2##, you only know that is true for ##\theta## itself. Also when you write it that way it implies both inequalities are true, but you proceed to split it into assuming one is true or the other is true.

It might help to just assume like, ##\theta=\pi/4## first just to see what the solution looks like.
 
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