What is the legal (Shar'i) method for a husband to take his wife back after he uttered "you are divorced" in a moment of extreme anger due to an argument? Is it by word, or by a new marriage contract? And is it necessary to document the divorce with a ma'dhun (authorized official)?

The first case is that anger caused you to lose consciousness and discernment. In this case, the divorce is not valid, and you must take your wife back; otherwise, the divorce will be binding.

Divorce becomes effective as soon as the husband pronounces it. The presence of a marriage officiant (ma'dhun) or the wife's knowledge of it is not a condition. It is recommended to have witnesses for the divorce to safeguard rights and prevent disputes.

The wife must confirm that the divorce has occurred before marrying another man.