Complex.arg_one_add_mem_Ioo

∀ {z : ℂ}, ‖z‖ < 1 → (1 + z).arg ∈ Set.Ioo (-(Real.pi / 2)) (Real.pi / 2)

The argument of 1 + z for z in the open unit disc is always in (-π / 2, π / 2).

Defined in: Mathlib.Analysis.SpecialFunctions.Complex.Arctan
Cited by: 1 results in Mathlib
Foundations: Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

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