As |z1|=|z2|=|z3|=|z4| it represents a square or a rhombus.
Let us consider that the points are:
z1=x + iy
z2=x - iy
z3=-x + iy
z4=-x – iy
from the above above points it is clear that |z1 |=|z2 |=|z3 |=|z4 |=(x^2 + y^2)^1/2
[(x^2 = y^2)^1/2 represents x square +y square whole power 1/2]
It is also clear that |z1 – z2|=|z2 – z3|=|z3 – z4|=|z4 – z1| that is the magnitude of sides is equal
z1 + z2 + z3 + z4= x + iy + x – iy + (-x + iy) + (-x -iy) = 0
therefore the above points which represents a square satisfied the given conditions .
hence the given conditions results in the formation of a square.
