If `z^2=-i` then is it true that `z=+1/sqrt2 (1-i)`

If z_(1)=iz_(2) and z_(1)-z_(3)=i(z_(3)-z_(2)), then prove that |z_(3)|=sqrt(2)|z_(1)|

If z_1=i z_2 and z_1-z_3=i(z_3-z_2) ,then prove that |z_3|=sqrt(2)|z_1|.

If z is a complex number having least absolute value and |z-2+2i|=1 ,then z= (2-1//sqrt(2))(1-i) b. (2-1//sqrt(2))(1+i) c. (2+1//sqrt(2))(1-i)"" d. (2+1//sqrt(2))(1+i)

If z is a complex number having least absolute value and |z-2+2i|=1 ,then z= (2-1//sqrt(2))(1-i) b. (2-1//sqrt(2))(1+i) c. (2+1//sqrt(2))(1-i)"" d. (2+1//sqrt(2))(1+i)

If z is a complex number having least absolute value and |z-2+2i|=1 ,then z= (2-1//sqrt(2))(1-i) b. (2-1//sqrt(2))(1+i) c. (2+1//sqrt(2))(1-i)"" d. (2+1//sqrt(2))(1+i)

If z=(1+i)/sqrt2 , then the value of z^1929 is

If z=(1+2i)/(2-i)-(2-i)/(1+2i), then what is the value of z^(2)+zbarz (i=sqrt(-1))

The number of values of z which satisfy both the equations |z-1-i|=sqrt(2) and |z+1+i|=2 is

z is complex number such that (z-i)/(z-1) is purely imaginary. Show that z lies on the circle whose centres is the point 1/2 (1+i) and radius is 1/sqrt2

If the ratio (z-i)/(z-1) is purely imaginary, prove that the point z lies on the circle whose centre is the point (1)/(2) (1+i) and radius is (1)/(sqrt2)