Number Theory T...

The locus represented by $$|z -1|=|z + i|$$ is

If $$\displaystyle z= (i)^{(i)^{(i)}}$$ where $$ i = \sqrt{-1}$$, then $$z$$ is equal to

If x and y are real then which one of the following is true

If $$|z -2 + i| = |z-3-i|$$, then the locus of z is

Which of the following number is composite?

Let $$\displaystyle \left| Z_{r}-r\right| \leq r,\forall r=1,2,3,.......n.$$ Then $$\displaystyle \left| \sum_{r=1}^{n} Z_{r} \right| $$ is less than

If $$z_1, z_2$$ and $$z_3$$ are complex numbers such that $$|z_1| = |z_2| = |z_3| = \left | \displaystyle \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right | = 1,$$ then $$|z_1 + z_2 + z_3|$$ is

Fill in the blanks.
Every composite number can be expressed as a product of ____, and this factorization is unique except for the order in which the prime factors occur.

The number of composite number between $$101$$ and $$120$$ are