Archmage's Spell Power gives you bonus to your caster level (this helps with checks made to overcome spell resistance, duration of the spell and other level dependent effects). It doesn't change the DC of your spells.
I think, that if you want the highest possible DC, you should try Wizard 5/Shadow Adept 5/Red Wizard of Thay 30 (+16 to DC, i think)
(I would sacrifice +1 DC for cool SA abilities and made build like this: wizard 5/shadow adept 7/red wizard of thay 28)