# Fungrim entry: 6c2b31

${z}^{n + 1} = {z}^{n} z$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}$
Alternative assumptions:$z \in R \;\mathbin{\operatorname{and}}\; R \in \operatorname{Rings} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}$
TeX:
{z}^{n + 1} = {z}^{n} z

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}

z \in R \;\mathbin{\operatorname{and}}\; R \in \operatorname{Rings} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("6c2b31"),
Formula(Mul(Equal(Pow(z, Add(n, 1)), Pow(z, n)), z)),
Variables(z, n),
Assumptions(And(Element(z, CC), Element(n, ZZGreaterEqual(0))), And(Element(z, R), Element(R, Rings), Element(n, ZZGreaterEqual(0)))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC