Question

Maybe it is too early for me to ask this question, but why .... ?

Answer 1

\(\large\color{black}{ \displaystyle \left|1+i\right|=\sqrt{2} }\)

Answer 2

(and so \(\large\color{black}{ \displaystyle \left|1-i\right|=\sqrt{2} }\) )

Answer 3

can someone explain this?

Answer 4

both \(1+i\) and\(1-i\) are \(\sqrt2\) units away from \(0\)

Answer 5

Is that because i is a rotation?

Answer 6

A 45 degree rotation?

Answer 7

just like both \((1,1)\) and \((1,-1)\) have distance \(\sqrt2\) from \((0,0)\)

Answer 8

or if you prefer, just like the diagonal of any square with side 1 has length \(\sqrt2\)

Answer 9

Wait, so i is a diagonal?