Does [z] + [j] equal [ ʒ ]?

Solution 1:

Yes, [z] + [j] → [ʒ]. The [z] is an alveolar sound (i.e. articulated at the alveolar ridge) while [j] is a palatal sound (articulated at the hard palate), so when [j] comes right after [z], it pulls the place of articulation of [z] towards the hard palate, making it [ʒ]. The technical term for this phenomenon is assimilation. In this case, it's assimilation of place (i.e. the place of articulation of one of the two adjacent sounds is changed). It doesn't always happen. Some speakers assimilate their sounds while others don't.

Other alveolar sounds that usually assimilate (merge) are:

• [s] + [j] → [ʃ]
• [d] + [j] → [d͡ʒ]
• [t] + [j] → [t͡ʃ]

You will also hear miss you being pronounced something like mishoo. In many words, assimilation has taken place historically, for example, mission, pleasure, gradual, feature etc (mostly monomorphemic words). In some words such as issue and azure, it has taken place for some speakers; others might pronounce them with [sj] and [zj] respectively. Also, as @Colin Fine pointed out in the comments below, it's dialectal and depends on individual speakers.