Gloria Zamudio appeals from the district court’s grant of the defendants’ motion to dismiss filed pursuant, to Fed.R.CivP. 12(b)(1), (5), and (6) and from the district court’s denial of her Fed.R.Civ.P. 59(e) motion. Zamudio argues that the dismissal of her complaint violated due process because she did not have notice of the filing of the defendants’ motion to dismiss prior to the dismissal of her complaint. She argues that the district court erred in 1) dismissing her complaint as a disciplinary sanc *80 tion; 2) denying her Rule 59(e) motion; and 3) dismissing her complaint with prejudice rather than without prejudice. Zamudio also argues that this court should address the issue whether an employee’s spouse has a right to file a claim with the EEOC against her spouse’s employer.

The certificate of service attached to the defendants’ motion to dismiss reflects that service on Zamudio was complete on February 26, 2004, when the defendants mailed it to Zamudio’s last known address. Fed.R.Civ.P. 5(b)(2)(B) (“Service by mail is complete upon mailing.”); accord, Vincent v. Consolidated Operating Co., 17 F.3d 782, 785 n. 9 (5th Cir. 1994). Zamudio has not shown that the district court abused its discretion in denying her Rule 59(e) motion, which argued lack of notice of the filing of the motion to dismiss as a ground for postjudgment relief. See Midland West Corp. v. FDIC, 911 F.2d 1141, 1145 (5th Cir. 1990). Zamudio’s argument that the district court’s dismissal was but a disciplinary sanction is conclusional and speculative.

Although Zamudio argues that a dismissal for lack of subject matter jurisdiction should be without prejudice rather than with prejudice, Zamudio does not challenge directly the district court’s dismissal of her complaint for lack of subject matter jurisdiction and/or for failure to state a claim. Arguments must be briefed to be preserved. Yohey v. Collins, 985 F.2d 222, 225-25 (5th Cir. 1993). When an appellant fails to address a potential error in the district court’s analysis, it is the same as if the appellant had not appealed the judgment. Brinkmann v. Dallas County Deputy Sheriff Abner, 813 F.2d 744, 748 (5th Cir. 1987). Zamudio has abandoned her challenge to the district court’s Rule 12(b) dismissal by failing to challenge the legal analysis forming the basis for the dismissal.

Zamudio asks this court to address the issue whether an employee’s spouse has a right to file a claim or complaint against her spouse’s employer with the United States Equal Employment Opportunity Commission. We decline to address this issue, the resolution of which was not necessary in the district court’s dismissal of Zamudio’s complaint.

AFFIRMED.