The high-velocity cloud ( HVC ) Complex A is a probe of the physical conditions in the Galactic halo . The kinematics , morphology , distance , and metallicity of Complex A indicate that it represents new material that is accreting onto the Galaxy . We present Wisconsin H \alpha  Mapper ( WHAM ) kinematically resolved observations of Complex A over the velocity range of -250 to -50 ~ { } { km \thinspace s ^ { -1 } } in the local standard of rest reference frame . These observations include the first full H \alpha  intensity map of Complex A across ( \mathit { l,b } ) = ( 124 \arcdeg, 18 \arcdeg ) to ( 171 \arcdeg, 53 \arcdeg ) and deep targeted observations in H \alpha , [ S ii ] \lambda 6716 , [ N ii ] \lambda 6584 , and [ O i ] \lambda 6300 towards regions with high H i column densities , background quasars , and stars . The H \alpha  data imply that the masses of neutral and ionized material in the cloud are similar , both being greater than 10 ^ { 6 } M _ { \odot } . We find that the model for the intensity of the ionizing radiation near the Milky Way is consistent with the known distance of the high-latitude part of Complex A and an assumed cloud geometry that puts the lower-latitude parts of the cloud at a distance of 7 to 8 \mathrm { kpc } . This compatibility implies a 5 % ionizing photon escape fraction from the Galactic disk . We also provide the nitrogen and sulfur upper abundance solutions for a series of temperatures , metallicities , and cloud configurations for purely photoionized gas ; these solutions are consistent with the sub-solar abundances found by previous studies , especially for temperatures above 10 ^ { 4 } ~ { } { K } or for gas with a high fraction of singly-ionized nitrogen and sulfur .