Complex Numbers...

If $$z_1+ z_2 + z_3 = 0$$ and $$|z_1|=|z_2|=|z_3|= 1$$, then area of triangle whose vertices are $$z_1, z_2$$ and $$z_3$$ is:

If $${z}_{1},{z}_{2},..{z}_{n}$$ lie on the circle $$|z|=2$$ then the value of $$|{z}_{1},{z}_{2},..{z}_{n}|-4|\dfrac {1}{{z}_{1}}+\dfrac {1}{{z}_{2}}++\dfrac {1}{{z}_{n}}|=$$

For $${ { Z }_{ 1 }=\sqrt [ 6 ]{ \dfrac { 1-i }{ 1+i\sqrt { 3 }  }  }  };\quad { { Z }_{ 2 }=\sqrt [ 6 ]{ \dfrac { 1-i }{ \sqrt { 3 } +i }  } ;\quad { { Z }_{ 3 }=\sqrt [ 6 ]{ \dfrac { 1-i }{ \sqrt { 3 } -i }  }  } }$$ which of the following holds good?

For a complex number $$z$$, the minimum value of $$\left | z \right |+\left | z-\cos\alpha-i\sin\alpha \right |$$ is

If $$Z_{1},Z_{2}$$ are two complex numbers satisfying $$|\dfrac{Z_{1}-3Z_{2}}{3-Z_{1}Z_{2}}|=1|z_{1}|\neq 3$$ then $$|z_{2}|=$$

$$|z-4| < |z-2|$$ represents the region given by?

If $$P(x)=a{x}^{2}+bx+c$$ and $$Q(x)=-a{x}^{2}+dx+c$$ where $$ac\ne 0$$, then $$P(x).Q(x)=0$$ has

The modulus of $$\overline { 6+{ i }^{ 3 } } +\overline { 6+{ i } }+\overline { 6+{ i }^{ 2 } } $$ is

If $$\left| z \right| =1$$ and $$\left| \omega -1 \right| =1$$ where $$z,\omega \in C$$ then the largest set of values of $${ \left| 2z-1 \right|  }^{ 2 }+{ \left| 2\omega -1 \right|  }^{ 2 }$$ equals 

The value of $$(z+3) (\overline{z} +3)$$ is eqquivalent to