Hello, 

I am attaching a code sample illustrating this approach. It contains two buttons and two igDialog instances.
It is possible to initialize the igDialog using Angular directives and setting the state option to be closed like    
<ig-dialog id="angularJS_igDialog" header-text="AngularJS Dialog" height="325px" state="closed">

This way when rendering the document, the igDialog will not be visible and when interacting with the buttons, respectively Show Dialog for the usual jQuery based igDialog implementation and Show AngularJS Dialog for the Angular declared one, you will observe the expected behavior.  http://jsfiddle.net/zcL5hmuz/3/

http://jsfiddle.net/damyanpetev/jxej5mtd/

Regards,

Damyan Petev

Associate Software Developer

Infragistics, Inc.