Which of the following statement(s) is (are) correct ?

Options

A. IF `|z|le4`, then maximum value of `|iz+3-4i|` is equal to 9
B. If `|z|le4`, then maximum value of `|iz+3-4i|` is equal to 8
C. `z_(1),z_(2),z_(3),z_(4)` are distinct complex numbers representing the vertices of a quadrilateral ABCD taken in order. If `z_(1)-z_(4)=z_(2)-z_(3)` and arg `(z_(4)-z_(1))/(z_(2)-z_(1))=(pi)/(2)`, then the quadrilateral is rectangle.
D. `z_(1),z_(2),z_(3),z_(4)` are distinct complex numbers representing the vertices of a quadrilateral ABCD taken in order. If `z_(1)-z_(4)=z_(2)-z_(3)` and arg `(z_(4)-z_(1))/(z_(2)-z_(1))=(pi)/(2)`, then the quadrilateral is rhombus .

Explanation

(A) `|iz+3-4i| le |iz|+|3-4i|=|z|+5 le 9`
The first condition implies that `(z_(1)+z_(3))/(2)=(z_(2)+z_(4))/(2)`
That is, diagonals AC is BD bisect each other.
Hence , quadrilateral is a parallelogram.
The second condition implies that the angle between AD and AB is `90^(@)`. Hence, the parallelogram is a rectangle.