Identify the region of the Argand diagram defined by `|z-1|+ |z+1| le 4`

Identify Z In the following sequence of reaction.

Let i= sqrt-1 . If a sequence of complex numbers is defined by z_(1)=0, z_(n+1)= z_(n)^(2)+i for n ge 1 , then find the value of z_(111) .

If the complex numbers z _(1) , z _(2) and z _(3) denote the vertices of an isosceles triangle, right angled at z _(1), then (z _(1) - z _(2)) ^(2) + (z _(1) - z _(3)) ^(2) is equal to A)0 B) (z _(2) + z _(3)) ^(2) C)2 D)3

Prov ethat the triangle formed by the points 1, (1+i)/(sqrt2) and i as vertices in the Argand diagram is isosceles.

If |z_(1)|= |z_(2)|= |z_(3)|=1 and z_(1) , z_(2), z_(3) are represented by the vertices of an equilateral triangle then which of the following is true?

Let f be the subset of Z xx Z defined by f = {(ab, a + b) : a,b in Z} is f a function from Z to Z? justify your answer.