Math 2.0

Field theory and polynomials Proposition

i squared is minus one

Builds on Imaginary unitComplex numbers

Statement

Let ii be the imaginary unit of ℂ\mathbb{C}. Then i2=−1i^2 = -1.

Remarks

With the product of complex numbers, (0+1i)(0+1i)=(0⋅0−1⋅1)+(0⋅1+1⋅0)i=−1(0 + 1 i)(0 + 1 i) = (0 \cdot 0 - 1 \cdot 1) + (0 \cdot 1 + 1 \cdot 0) i = -1. Also (−i)2=−1(-i)^2 = -1. Thus −1-1 has the two square roots ii and −i-i in ℂ\mathbb{C}.

Reading path

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Where this leads

3 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Imaginary_unit, Definition
About this page
Tag07KBQCG9KV
URIm2://07KBQCG9KV
Kindstatement, proposition
WritingW0 stub
MSC12D99
StatusThis copy of the site has no build data. Run m2 status 07KBQCG9KV.
UsesImaginary unit, Complex numbers

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