Bioinformatics tool for "pairwise alignment" of complementary sequences?
I'm not sure this is what you need since the sequences you posted are not actually complementary as far as I can tell. However, exonerate is one of the most powerful tools out there and can do this as well. Using these sequences as examples:


  >query
  TAGCTTATTGATGGGAGGAGAGTCCGTGCACATGACAGACCTTGGCTGTCCCAGACTGCAGGAAGCCCAGG
  >target
  CCTGGGCTTCCTGCAGTCTGGGACAGCCAAGTCTGTTATGTGCACGTACTCTCCTCCCCTCAATAAGCTA


And this command (should be run on a *nix system):

exonerate -m coding2coding -q qq.fa -t test.fa -s 0


I get this output:

C4 Alignment:
------------
         Query: query [revcomp]
        Target: target
         Model: genome2genome
     Raw score: 312
   Query range: 71 -&gt; 0
  Target range: 0 -&gt; 70

 71 :                                                          CCA       :  6
      CCTGGGCTTCCTGCAGTCTGGGACAGCCAAGGTCTGTCATGTGCACGGACTCTCCTCProTCAATA
      |||||||||||||||||||||||||||||| |||||| ||||||||| |||||||||||+||||||
      CCTGGGCTTCCTGCAGTCTGGGACAGCCAA-GTCTGTTATGTGCACGTACTCTCCTCProTCAATA
  1 :                                                          CCC       : 65

  5 : AGCTA :  1
      |||||
 66 : AGCTA : 70

vulgar: query 71 0 - target 0 70 + 312 M 30 30 G 1 0 M 26 26 C 3 3 M 11 11

C4 Alignment:
------------
         Query: query
        Target: target [revcomp]
         Model: genome2genome
     Raw score: 309
   Query range: 0 -&gt; 71
  Target range: 70 -&gt; 0

  1 :                      GTC                                           : 66
      TAGCTTATTGATGGGAGGAGAValCGTGCACATGACAGACCTTGGCTGTCCCAGACTGCAGGAAGC
      ||||||||||| |||||||||||+||||||||| ||||| ||||||||||||||||||||||||||
      TAGCTTATTGAGGGGAGGAGAValCGTGCACATAACAGA-CTTGGCTGTCCCAGACTGCAGGAAGC
 70 :                      GTA                                           :  6

 67 : CCAGG : 71
      |||||
  5 : CCAGG :  1

vulgar: query 0 71 + target 70 0 - 309 M 21 21 C 3 3 M 15 15 G 1 0 M 31 31


Basically it gives you two alignments, one reading the target 3->5 and the query 5->3 and one the other way around. 

Alternatively, you could do a translated blast search, tBLASTx which will translate both target and query sequence and so, should find complementary regions.