If `(1+i)z=(1-i)barz`, then show that `z = -ibar(z)`

If iz^3+z^2-z+i = 0 , then show that |z|=1.

If I_(n)=int z^(n)e^(1//z)dz , then show that (n+1)! I_(n)=I_(0)+e^(1//z)(1!z^(2)+2!z^(3)+...+n!z^(n+1)) .

If the complex number z_1 and z_2 be such that arg(z_1)-arg(z_2)=0 , then show that |z_1-z_2|=|z_1|-|z_2| .

If z=x+i y is a complex number with x ,y in Qa n d|z|=1, then show that |z^(2n)-1| is a rational number for every n in Ndot

If z = x + iy and w=(1-iz)/(z-i) , show that : |w|=1 implies z is purely real.

If (3+i)(z+bar(z))-(2+i)(z-bar(z))+14i=0 , where i=sqrt(-1) , then z bar(z) is equal to

If (3+i)(z+bar z)-(2+i) (z- bar z)+14i=0 , then z bar z =

If z=x+iy and |z|=1, show that the complex number z_1=(z-1)/(z+1) is purely imagine.

If |z-iRe(z)|=|z-Im(z)|, then prove that z lies on the bisectors of the quadrants, " where "i=sqrt(-1).

Define addition and multiplication of two complex numbers z_1 and z_2 . Hence show that : I_m (z_1+ z_2)=I_m (z_1)+I_m(z_2) .