No
No it shouldn't be capitalized.
Yes, you capitalize "the" when it is part of a proper noun or title.
It is capitalized at the beginning of the sentence or when it forms part of the proper noun. Examples: The 2nd century is considered part of the Classical era. The Second Century Initiative is celebrating its anniversary.
Real part of the result = real part of first number + real part of second number Imaginary part of the result = imaginary part of first number + imaginary part of second number
You capitalize Judge Smith. You do not need to capitalize retired as it is not part of his title.
No, unless it's part of a name--for example, The Second Nondenominational Community Church." But: "The church I attend is nondenominational."
No, you do not have to capitalize the word "female" unless it is at the beginning of a sentence or part of a title.
You capitalize it when it's part of a proper name, e.g. Treaty of Paris.
You capitalize all rank that is part of a title, for instance:Private QunicySergeant JonesCaptain WallyIt is not necessary to capitalize rank that is not part of a title, for instance."John wanted to become a sergeant in the US Army."
No, you do not capitalize the colors when referring to objects unless they are part of the proper noun or name of the object. For example, "the red building" and "the blue building" would not be capitalized.
You only capitalize it if it is part of a proper noun. The FBI is the Federal Bureau of Investigation.
Capitalize the word architect only when it is part of a title.Example:Senior Architect, Joe Smith