Number Theory T...

If $$z_{1},\ z_{2}$$ are two complex numbers such that $$arg\left( { z }_{ 1 }+{ z }_{ 2 } \right) =0$$ and $$Im\left( { z }_{ 1 }{ z }_{ 2 } \right) =0$$, then

$$\sqrt{-2}\sqrt{-3}=$$

If $$\left| z \right| = 1$$, then $$\left| z - 1 \right|$$ is

If z is a complex number such that $$|z|\ge 2$$, then the minimumm value of $$\left|z+\dfrac{1}{2}\right|$$:

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

If $$Z$$ is a complex number such that $$|z| \ge 2$$,
then the minimum value of $$\left|z + \dfrac{1}{2}\right|$$

If $$\left| {\dfrac{{{z_1}}}{{{z_2}}}} \right| = 1$$ and $$\arg \left( {{z_1}{z_2}} \right) = 0$$ , then

$$I_m$$ $$\left( {\sqrt {a + i\sqrt {{a^4} + {a^2} + 1} } } \right) = $$

If for complex number $$z_{1}and   z_{2}arg(z_{1})-arg(z_{2})=0then \mid z_{ 1}-z_{2}\mid $$ is equal to:

Argument and modules of $$[\dfrac{1+i}{1-i}]^{2\pi i}$$ are respectively.................