complicate
to make (something) more difficult to deal with, do or understand
 Three of the dinner guests don't eat meat, two are on a diet and just to complicate matters /things, the sixth is allergic to milk.
 It will only complicate the situation /issue if we invite his old girlfriend as well.
 The rescue operation has been complicated by bad weather.
 The new rules have complicated the tax system even further.

 If something, esp. an illness, complicates another illness, it makes the other illness worse. 
 His breathing problem has been complicated by a chest infection.

complicated
 The relationship is a bit complicated. He's my mother's cousin's daughter's child.
 This machine looks a bit too complicated for my liking.
 I had to fill in this really complicated form.
 The rules are rather complicated to follow.

complication
A complication is something which makes a situation more difficult. 
 Dave couldn't find his passport at the airport and then there were further complications when Fiona lost her baggage.
 Have you thought of the practical complications of doing what you suggest?
 If any complications arise, let me know and I'll help.

A complication is also an additional medical problem which makes it more difficult to treat an existing illness.
 If there are no complications, the doctor says that she'll be able to come home within two weeks.