2 fixed a typo ("Mathemathics" versus "mathematics"); deleted 14 characters in body
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As reported by the NOAD, the meaning of those words are:

complicated /ˈkɑmpləˌkeɪdɪd/
adjective
1. consisting of many interconnecting parts or elements; intricate: a complicated stereo system.
• involving many different and confusing aspects: a long and complicated saga.
2. Medicine involving complications: complicated appendicitis.

complex
adjective /ˌkɑmˈplɛks/
1. consisting of many different and connected parts: a complex network of water channels.
• not easy to analyze or understand; complicated or intricate: a complex personality, the situation is more complex than it appears.
2. Mathematics denoting or involving numbers or quantities containing both a real and an imaginary part.
3. Chemistry denoting an ion or molecule in which one or more groups are linked to a metal atom by coordinate bonds.

The meaning of complex partially coversoverlaps the meaning of complicated; the difference is that complex is also used as noun, and that it is used in specific contexts with a specific meaning (see Chemistry, and MathemathicsMathematics).

As reported by the NOAD, the meaning of those words are:

complicated /ˈkɑmpləˌkeɪdɪd/
adjective
1. consisting of many interconnecting parts or elements; intricate: a complicated stereo system.
• involving many different and confusing aspects: a long and complicated saga.
2. Medicine involving complications: complicated appendicitis.

complex
adjective /ˌkɑmˈplɛks/
1. consisting of many different and connected parts: a complex network of water channels.
• not easy to analyze or understand; complicated or intricate: a complex personality, the situation is more complex than it appears.
2. Mathematics denoting or involving numbers or quantities containing both a real and an imaginary part.
3. Chemistry denoting an ion or molecule in which one or more groups are linked to a metal atom by coordinate bonds.

The meaning of complex partially covers the meaning of complicated; the difference is that complex is also used as noun, and that it is used in specific contexts with specific meaning (see Chemistry, and Mathemathics).

As reported by the NOAD, the meaning of those words are:

complicated /ˈkɑmpləˌkeɪdɪd/
adjective
1. consisting of many interconnecting parts or elements; intricate: a complicated stereo system.
• involving many different and confusing aspects: a long and complicated saga.
2. Medicine involving complications: complicated appendicitis.

complex
adjective /ˌkɑmˈplɛks/
1. consisting of many different and connected parts: a complex network of water channels.
• not easy to analyze or understand; complicated or intricate: a complex personality, the situation is more complex than it appears.
2. Mathematics denoting or involving numbers or quantities containing both a real and an imaginary part.
3. Chemistry denoting an ion or molecule in which one or more groups are linked to a metal atom by coordinate bonds.

The meaning of complex partially overlaps the meaning of complicated; the difference is that complex is also used as noun, and in specific contexts with a specific meaning (see Chemistry, and Mathematics).

1
source | link

As reported by the NOAD, the meaning of those words are:

complicated /ˈkɑmpləˌkeɪdɪd/
adjective
1. consisting of many interconnecting parts or elements; intricate: a complicated stereo system.
• involving many different and confusing aspects: a long and complicated saga.
2. Medicine involving complications: complicated appendicitis.

complex
adjective /ˌkɑmˈplɛks/
1. consisting of many different and connected parts: a complex network of water channels.
• not easy to analyze or understand; complicated or intricate: a complex personality, the situation is more complex than it appears.
2. Mathematics denoting or involving numbers or quantities containing both a real and an imaginary part.
3. Chemistry denoting an ion or molecule in which one or more groups are linked to a metal atom by coordinate bonds.

The meaning of complex partially covers the meaning of complicated; the difference is that complex is also used as noun, and that it is used in specific contexts with specific meaning (see Chemistry, and Mathemathics).