C# :: Cannot Update Text In Richtextbox Using Class

It's my understanding that there are three ways to go about updating a control on a form from a class.

A) Instance the form, eg: Form1 Frm = new Form1();
The problems I have run into with this is that while writing text to a richtextbox using the instance Frm, the richtextbox never updates on the form.

B) Passing the object to the class.
This method seems less used and can be very problematic. Haven't looked into it thoroughly.

C) Exposing the objects using classes within the Form.
While making methods public they still do now show as available for use when calling from classes, unless I instance them but then I run into problem A. I've considered making the methods static so no instancing is required but when doing so the object(in this case richtextbox) becomes invalid due to itself being instanced by the automatically generated code when adding the object.

I know there is another way to pass values then force the object to update but that won't necessarily work with a richtextbox as you have the option to deal with color and font variations.

I imagine I'm missing something pretty simple here but I can't find any resources online about how to handle objects with more complex data than just straight text.

Example of problem A

//called from a class
Form1 Chat = new Form1();
Chat.BeginChat();
Chat.AddChat(Color.Lime, "Testing");
Chat.EndChat();

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