No person shall be eligible for an elective office of the city unless at the time of election the person is a qualified elector within the meaning of the state constitution and has resided in the city during the six months immediately preceding the election. If the person is a resident of an area annexed less than six months prior to election, total continuous residency in the area annexed shall be counted towards the 6-months requirement. The council shall be final judge of the qualifications and election of its own members.