Number Theory T...

If $$|Z|=2,|z_{2}|=3,|z_{3}=4|$$ and $$|z_{1}+z_{2}+z_{3}|=5$$ then $$|4z_{2}z_{3}+9z_{3}z_{1}+16z_{1}z_{2}|=$$

If $$\dfrac{x - 3}{3 + i} + \dfrac{y - 3}{3 - i} = i $$ where $$x , y \in R$$ then

The locus of $$z$$ such that $$\left| {\dfrac{{z + i}}{{z - 1}}} \right| = 2$$

If $$\left| {z - 1} \right| = 2$$, then the value of $$z\overline z  - z - \overline z $$ is equal to: 

If z is a complex number such that $$\left|\dfrac{z-3i}{z+3i}\right|=1$$ then z lies on?

$$\left(\dfrac{1 + i}{1 - i}\right)^4 + \left(\dfrac{1 - i}{1 + i}\right)^4 = $$ 

If $$|z_1+z_2|=|z_1|+|z_2|$$ where $$z_1$$ and $$z_2$$ are different non - zero complex number, then ?

The complex number $$z$$ satisfies $$z+|z|=2+8i$$. The value of $$|z|$$ is

The number of prime numbers between $$1 \ and \ 10$$ is

if $$z_1=3+4i$$ and $$Im(z_1z_2)=0$$ Find $$z_2$$