Number Theory T...

The number of non-zero integral solution of the equation $$ \left | \sqrt{3}+i \right |^{x}= 2^{x} $$

If $$z=4+i\sqrt7$$, then value of $$z^3-4z^2-9z+91$$ equals

Write all the composite numbers between $$10$$ and $$35.$$

$$\displaystyle \left [ \left ( \cos \theta +i \sin \theta \right )\left ( \cos \theta -i\sin \theta  \right ) \right ]^{-1}$$

If $$\displaystyle \log _{ \sqrt { 3 }  }{ \left( \frac { { \left| z \right|  }^{ 2 }-\left| z \right| +1 }{ 2+\left| z \right|  }  \right)  } <2$$, then the locus of $$z$$ is 

Solve : $$(2-\sqrt{-100})(1+\sqrt{-36})$$

If $$Re(a), \space Re(b) > 0$$, and $$x = |a - b| - |\bar{a} + b|$$, then

If $$z = re^{i\theta}$$, then the value of $$|e^{iz}|$$ is equal to

Find the modulus and amplitude of $$-2i$$