Question

express a+ib (-2-⅓i)³

Answer 1

(-2-1/3i)³ = (-1)³(2+i/3)³

            = - [(2)³+(i/3)³+3(2)(i/3)(2+i/3)]          [ since (a+b)³ = a³+b³+3ab(a+b) ]

           = -[8+(i³/27)+2i(2+i/3)]

          = -[8+(-i/27)+4i+(2i²/3)]                      [ since i³ = - i ]

          = - [8+(-i/27)+4i+(-2/3)]                      [ since i² = - 1 ]

         = - [8+(-2/3)+i(4-1/27)]

         = - [22/3 +i(107/27)]

        =  (-22/3)+i( -107/27)