Question

the notation \(\mathbb{C}^{*}\) is used for the set \(\mathbb{C} ~ \backslash ~ \{(0,0)\}\).

can anyone explain what that means?

Answer 1

especially the \(\backslash \)

Answer 2

It is the entire complex plane WITHOUT 0 (the origin).
\ means: leave out from the set.

Answer 3

ah! now I recall again that \(\mathbb{R^*}\) is the set of reals without zero. must be related

Answer 4

Because \ is always between sets, the complex number 0, that could bee looked upon as the point (0, 0) is put between curly brackets.