Does modular arithmetic have different rules for different cases?

[Bipolarity]

Homework Statement

I'm trying to prove the following (as part of an isomorphism problem).
The problem is I don't know much about modular arithmetic, so would appreciate some help.

$$2((a+b)mod \ 2π) = (2a+2b)mod \ 4π.$$

given that a,b are both nonnegative and less than 2π.

Homework Equations

The Attempt at a Solution

I believe there are certain identities for modular arithmetic that I could use, but do not know. Can anyone tell me some or give me a link to some modular arithmetic identities? Thanks.

BiP

 

[Dick]

Homework Statement

I'm trying to prove the following (as part of an isomorphism problem).
The problem is I don't know much about modular arithmetic, so would appreciate some help.

$$2((a+b)mod \ 2π) = (2a+2b)mod \ 4π.$$

given that a,b are both nonnegative and less than 2π.

Homework Equations

The Attempt at a Solution

I believe there are certain identities for modular arithmetic that I could use, but do not know. Can anyone tell me some or give me a link to some modular arithmetic identities? Thanks.

BiP

Break it into cases i) 0<=(a+b)<2pi and ii) 2pi<=(a+b)<4pi.