Number Theory T...

The number $$111111111$$ is a

If $$(1+i)^{-20}=a+ib$$, then the values of $$a$$ and $$b$$ are

Find the which of the complex number has greatest modulus.

If $$\dfrac {z-1}{z+1}$$ is purely imaginary then 

 For any complex number $$z$$ the minimum value of $$|z|+|z-2013i|$$ is...

If $$z=x+iy(x,y\epsilon R,x\neq -1/2),$$ the number of values of z satisfying $$\left | z \right |^{n}=z^{2}\left | z \right |^{n-2}+1.(n\epsilon N,n> 1)$$is

$$z_{1}$$ and $$z_{2}$$ are two non-zero complex numbers such that $$|z_{1}|=|z_{2}|$$ and $$argz_{1}+argz_{2}=\pi$$, then $$z_{2}$$ equals 

If $$ z=1+i\sqrt { 3, } \left| arg\left( z \right)  \right| +\left| arg\left( \overline { z }  \right)  \right|$$

If arg $$\left( {{Z_1} + {Z_2}} \right) = 0\;$$ and $$|{z_1}|\; = \;|{z_2}|\; = 1.$$ then.

The value of $${\left( {1 + i} \right)^5} \times {\left( {1 - i} \right)^5}$$ is