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The activated complex is basically the transition state which is the state at which bonds are being both broken and formed. In order to draw the activated complex, you would draw the molecule with its changing bonds, inserting dotted lines where new bonds are forming and where bonds are breaking to indicate that it is in the transition of going through the reaction. The activated complex occurs at the highest, most unstable potential energy point of the reaction and is visually seen as the top of the peak of a graph of the reaction's progress.
The activated complex refers to the transition state. Based on reactants and products as given, the transition state can be figured out (which atom should be linked to which atom etc.)
Activated complex is the transition state of a reaction. Basically, an electronegative atom breaks off from a molecule and a nucleophile comes to take its place. In the transition state, you would use dotted lines to represent formed/broken bonds. This is what people refer to as the double dagger
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