Principal value of an argument

[user12323567]

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

 

[haruspex]

What is the definition of the principal value of an angle?

 

[Office_Shredder]

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.