If `z!=0` is a complex number, then prove that `R e(z)=0 rArr Im(z^2)=0.`

If z is a complex number such that Re (z) = Im(z), then

If z is a complex number such that Re(z)=Im(z) , then

For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

If z^(2)+z+1=0 , where z is a complex number, then the value of (z+(1)/(z))^(2)+(z^(2)+(1)/(z^2))^(2)+(z^(3)+(1)/(z^3))^(2)+"……"+(z^(6)+(1)/(z^6))^(2) is

If z_1a n dz_2 are two complex numbers and c >0 , then prove that |z_1+z_2|^2lt=(1+c)|z_1|^2+(1+c^(-1))|z_2|^2dot

The three angular points of a triangle are given by Z=alpha, Z=beta,Z=gamma,w h e r ealpha,beta,gamma are complex numbers, then prove that the perpendicular from the angular point Z=alpha to the opposite side is given by the equation R e((Z-alpha)/(beta-gamma))=0

If z = + iy is complex number such that Im ((2z + 1)/(iz + 1)) = 0, show that the locus of z is 2x^(2) + 2y^(2) + x - 2y = 0.

If Z^5 is a non-real complex number, then find the minimum value of | (Imz^5)/(Im^5z) |

If z is non zero complex number, such that 2i z^(2) = bar(z), then |z| is

Find the complex number z satisfying R e(z^2) =0,|z|=sqrt(3.)