structure of the complex formed by iodine and starch

The Iodine test is used to test for the presence of starch. Iodine solution — iodine dissolved in an aqueous solution of potassium iodide — reacts with starch producing a deep blue-black color.
This reaction is the result of the formation of polyiodide chains from the reaction of starch and iodine. The amylose, or straight chain portion of starch, forms helices where iodine molecules assemble, forming a dark blue/black color. The amylopectin, or branched portion of starch, forms much shorter helices and iodine molecules are unable to assemble, leading the colour to be of an orange/yellow hue. As starch is broken down or hydrolyzed into smaller carbohydrate units, the blue-black color is not produced. Therefore, this test can determine completion of hydrolysis when a color change does not occur.

Amylose is a linear polymer of glucose linked with mainly α(1→4) bonds. It can be made of several thousands of glucose units. It is one of the two components of starch, the other being amylopectin.

Amylose structure
The α(1→4) bonds promote the formation of a helix structure. The structural formula of amylose is pictured at right. The number of repeated glucose subunits (n) can be many thousands (usually in the range of 300 and 3000).
Amylose starch is less readily digested than amylopectin. However it takes up less space so is preferred for storage in plants; it is about 20% of the starch in plants is stored. The digestive enzyme amylase works on the ends of the starch molecule, breaking it down into sugars.
Iodine molecules fit neatly inside the helical structure of amylose, binding with the starch polymer, causing it to absorb certain wavelengths of light. Hence, a common test for starch is to mix it with a small amount of yellow iodine solution. In the presence of amylose a blue-black colour will be observed. The intensity of the colour can be tested with a colorimeter using a red filter, to indicate the concentration of starch present in the solution.
I hope this can help your understanding. =)

structure of the complex formed by iodine and starch is i-starch (presumable intelligent starch).