# Line in CP_2

I am confused with the following definitions:

I) (Projective) Line in CP_2

II) Hyperplane in CP_2

III) Straight line in CP_2

IV) Plane (projective?) in CP_2

I am sure that II and III are two different objects but I have the following questions:

I) (Projective) Line in CP_2

II) Hyperplane in CP_2

III) Straight line in CP_2

IV) Plane (projective?) in CP_2

I am sure that II and III are two different objects but I have the following questions:

Update:
A) The parameter, say t, for III is a real number. If t is complex number, it will become a totally different geometric object. What is the name of this object?

B) Are I and IV two different objects? Is I ( or IV ) different from II and III ?

B) Are I and IV two different objects? Is I ( or IV ) different from II and III ?

Update 2:
已經收到，答案消化中...基本上我應該攪錯左，係無 real straight line 哩回事...

Update 3:
Dear Ivan,

..., there are "less direction" in C^3 than R^6, so that even though it is a R^4,...(*)

What is the meaning of above? Any example?

Also, is below just the same as (*) ?

A) In general, there are more real plane than complex line

..., there are "less direction" in C^3 than R^6, so that even though it is a R^4,...(*)

What is the meaning of above? Any example?

Also, is below just the same as (*) ?

A) In general, there are more real plane than complex line

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