Introduction

Complex Numbers

Numbers of the form x + iy do not constitute an ordered field e.g. a + ib > c + id or a + ib < c + id does not make any sense.

Square roots of unity are represented as ± 1, cube roots of unity are 1, ω, ω₂

Four fourth roots of unity are ± 1, ± i.

It is this symbol i that is defined as √-1  in order to extend the number system from real to complex field and it has the property that

i² = −1, i⁴ = 1, i²⁰¹ = i^{4 × 50} + 1 = i