If `arg (z^(1//3))=(1)/(2)arg(z^(2)+barzz^(1//3)),` find the value of `|z|.`

If |z+1|=z+2(1+i) then find the value of z.

If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(2) and (x-1)/(3k)=(y-1)/(1)=(z-6)/(-5) are perpendicular, find the value of k.

If z=(1+i)/(√2) , then the value of z^(1929) is

If (z-1)/(z+1) is purely imaginary number (zne-1) then find the value of |z|.

If z_(1),z_(2)inC,z_(1)^(2)+z_(2)^(2)inR,z_(1)(z_(1)^(2)-3z_(2)^(2))=2 and z_(2)(3z_(1)^(2)-z_(2)^(2))=11, the value of z_(1)^(2)+z_(2)^(2) is

If z=(1)/((2+3i)^(2)) then |z|=...

If |z_1-1|lt=1,|z_2-2|lt=2,|z_(3)-3|lt=3, then find the greatest value of |z_1+z_2+z_3|dot

If |z|ge3, then determine the least value of |z+(1)/(z)| .

If z=3-2i then show that z^(2)-6z+13=0 Hence find the value of z^(4)-4z^(3)+6z^(2)-4z+17

If omega = z//[z-(1//3)i] and |omega| = 1 , then find the locus of z.