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

If z=(-1-i) , then arg z =

If z=x+iy, then show that z bar z + 2(z + bar z ) + b =0 represents a circle.

Select and write the correct answer from the given alternatives in each of the following: If (1 + i) z = 1 (1 - i) bar z , then z is

If abs(z+1) = z+2 (1+i), then find z

If abs(z_1) =1, ( z_1 != -1) and z_2 = frac{z_1 - 1}{z_1 +1} , then show that the real part of z_2 is zero.

If the real part of frac{bar z + 2}{bar z -1} is 4, then show that the locus of the point representing z in the complex plane is a circle.

If arg(z) = theta , then arg(bar z) =

If abs(z_1) = abs(z_2) = ........= abs(z_n) =1, then show that abs(z_1+ z_2+.......+z_n) = abs(frac{1}{z_1}+frac{1}{z_2}+.........frac{1}{z_n})

If arg(z)= theta , then arg( bar z ) = ?

If abs(z-3+ i) = 4 then, the locus of z is