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