The complex multiplication of the complex number \((0,1)\) is \((-1,0)\), i.e.
\[(0,1)\cdot(0,1)=(-1,0).\] We set \[i:=(0,1)\in\mathbb C\] and call the complex number \(i\) the imaginary unit. Because the complex number \((-1,0)\in\mathbb C\) can be identified with the real number \(-1\in\mathbb R\), we have \[i^2=-1.\]
Proofs: 1
Algorithms: 1
Definitions: 2
Explanations: 3
Lemmas: 4 5 6
Proofs: 7 8 9 10
