Learn English – Is ‘She has been taken’ active or passive voice

The sentence may recount the same facts, or it may not. One very significant difference is that in the active voice you must identify the Agent: the person (or other entity) who performs the action, whereas in the passive you are free to omit the Agent.

Active

^ok John stole my book.
^∗  Stole my book.

Passive

^ok My book was stolen by John.
^ok My book was stolen.

In either case, the passive voice is employed to focus on the Patient of the action—the person or thing which 'suffered' it—rather than on Agent who or which performed it. There are several reasons you might want to do this:

• Because you don’t know or don’t care who performed the action
• Because what is important is the action itself rather than who performed it
• Because what is important is the result of the action rather than who performed it
• Because you want your readers to think of the action as 'impersonal'

The last reason became particularly important in the 19th century, when scientific writers—or writers who wanted to be thought of as adopting a 'scientific' attitude—were particularly careful to banish any suggestion that the writer's personality or attitudes had any influence on what was reported. The passive voice remains to this day something of a fetish in the sciences, particularly in the 'soft' sciences, where there is still substantial anxiety about the scientific status and value of the work done.

^∗  marks an utterance as ungrammatical.

This is a silly question. It asks one to do something that can't be done.
The sentence

• I must go and look for my brothers.

is Intransitive, but Passive can only apply to a Transitive clause.

The Passive rule promotes the direct object to subject, demotes the old subject to an optional object of by, and adds the auxiliary verb be before the past participle form of the main transitive verb. Like this:

• Marie shot my cousin. == Passive => My cousin was shot (by Marie).

But if the clause isn't transitive, there isn't a direct object to promote, and other noun phrases don't usually work.

• Mary slept all day. but not *All day was slept (by Mary).

Sometimes prepositional objects can be passivized, if the preposition is one that makes a transitive verb out of an intransitive one, like look (at) or listen (to)

• We must look at/listen to that again. == Passive => That must be looked at/listened to again.

But that's rarely the case, so most prepositions after verbs don't mark direct objects. And without a direct object, Passive is impossible.

The real solution is to get a new textbook that actually describes English, instead of something like English.