Number Theory T...

Choose the composite numbers from the following numbers $$87, 67, 45, 34, 23, 27, 33$$.

If $$z$$ is a complex number, then $$z^{2}+\bar{z}^{2}=2$$ represents-

The modulus of the complex number $$z=\frac { \left( 1-i\sqrt { 3 }  \right) \left( \cos { \theta  } +isin\theta  \right)  }{ 2\left( 1-i \right) \left( \cos { \theta  } -isin\theta  \right)  } $$  is-

If $$x^{2}+y^{2}=1$$ and $$x \neq -1$$ then $$\dfrac {1+y+ix}{1+y-ix}$$

If $$\left|z\right|=1$$ and $$\varpi=\dfrac{z-1}{z+1}$$, where $$z\neq-1$$, then $$Re\left(\varpi\right)$$ is

What is the modulus of following complex number:$$-2+2\sqrt { 3i } $$

If $$z=(3+7i)(p+iq)$$ where $$p,q\in I-\left\{ 0 \right\} $$, is purely imaginary then minimum value of $${ \left| z \right|  }^{ 2 }$$ is

If $$z=(3+7i)(p+iq)$$, where $$p,q\in I-\left\{ 0 \right\} $$, is a purely imaginary, then minimum value of $${ \left| z \right|  }^{ 2 }$$ is

$$z=a+ib$$, $$a,b,\in R$$, $$b\ne 0$$ and $$\left| z \right| =1$$, then $$z=\cfrac{c+i}{c-i}$$, where $$c$$ is equal to

If $$z=\dfrac{\sqrt{3}}{2}+\dfrac{1}{2}i$$ then $$z\bar{z}$$ is