Connect motor in 220 VAC single phase (Line - Neutral) or in 110VAC two phases (110VAC - 110VAC "180 degree out of phase")?
Normal 120/240V residential power in North America comes from a center-tapped 240V single phase transformer secondary - the centre tap is grounded and is the &quot;Neutral&quot; connection.  No need for your complex clalculations to prove that you can get 240 V.
You can safely connect your 240 V motor to the two 120 V &quot;hot&quot; wires.