Step 1: Understanding the oxidation number of iron in the complex.
In the complex K\(_3\)[Fe(CN)\(_6\)], the cyanide ion (CN\(^-\)) is a monodentate ligand with a charge of -1. Since there are six cyanide ions, the total charge from the cyanide ions is -6. The overall charge of the complex is 0, so the charge on the iron atom must balance the -6 from the cyanides. This means the oxidation state of iron (Fe) is +3.
Step 2: Analyzing the options.
(A) -6: This is incorrect. Iron cannot have an oxidation number of -6 in this complex.
(B) -3: This is incorrect. Iron in this complex has a positive oxidation number.
(C) +3: This is correct. The oxidation state of iron in this complex is +3.
(D) +6: This is incorrect. The oxidation number of +6 would result in an incorrect charge balance.
Step 3: Conclusion.
The correct answer is (C) +3.