When and where did the real Macbeth reign?

Mac Bethad mac Findlaích (Modern Gaelic: MacBheatha mac Fhionnlaigh, anglicised as Macbeth, and nicknamed Rí Deircc, "the Red King" ) died 15 August 1057) was King of the Scots (also known as the King of Alba, and earlier as King of Moray and King of Fortriu) from 1040 until his death.