4.7 Regarding 2 2 as part of a complex plane , fix an angle ???? and...

4.7 Regarding ℤ2 ⊂ ℝ2 as part of a complex plane ℂ, fix an angle ???? and set

 = {

t ∈ Z2 ∶ t ≠ 0, ???? ≤ arg t < ???? + ????

}

, where arg t is shorthand for arg(t[1] + it[2]). Note that arg t and ???? are angles; if they are treated as numbers in [0,2????), then the above angular inequality is equivalent to the numerical conditions ???? ≤ arg t < ???? + ???? or

???? ≤ 2???? + arg t < ???? + ????. Show that  is a half-space.