Complex knots are intricate arrangements of loops and twists in a rope or string that cannot be untangled without cutting. They are studied in the field of topology, a branch of mathematics that explores the properties of space. Knots can be classified based on their structure, with some being more complicated than others, such as the trefoil knot or the figure-eight knot. In addition to their mathematical significance, complex knots have practical applications in various fields. For example, they are used in sailing for securing ropes, in rock climbing for safety, and in surgery for tying sutures. Understanding these knots helps improve techniques in both recreational and professional settings.