3. Suppose that f(z) = x² − y² −2y+i (2x-2xy), where z = x+iy. Use the expressions (see Sec. 6) x = z┼え 2 Z - Z and y = 2i to write f(z) in terms of z, and simplify the result. Ans. f(z)²+2iz.

10. Prove that a finite set of points Z1, Z2, Zn cannot have any accumulation points.

6. Show that a set S is open if and only if each point in S is an interior point.

2. Derive the component transformation equations for tensors shown be- low where [C] = [BA] is the direction cosine matrix from frame A to B. B[T] = [C]^[T][C]T 3. The transport theorem for vectors shows that the time derivative can be constructed from two parts: the first is an explicit frame-dependent change of the vector whereas the second is an active rotational change of the vector. The same holds true for tensors. Starting from the previous result, derive a version of transport theorem for tensors. [C] (^[T])[C] = dt d B dt B [T] + [WB/A]B[T] – TWB/A] (10 pt) (7pt)

Shade the areas given

of prove- Let (X, Td) be aspace. show that if A closed set in X and r & A, thend (r,A) +0

Q/prove:- Let (X, Td) be aspace. show that if a ex, then {a} is closed set (every finit set is closed set).

Already got wrong chatgpt answer Plz don't use chatgpt answer will upvote

not use ai please