Number Theory T...

 lf $$\log_{\frac{1}{2}}|\mathrm{z}-2|>\log_{\frac{1}{2}}|z|$$ then

The minimum value of $$f(z)=|\mathrm{z}|+|\mathrm{z}-1|+|z+2|$$ is

The real value of $$\theta$$ for which the expression, $$\displaystyle \frac{1+i\cos\theta}{1-2i\cos\theta}$$ is real number is

The region represented by z such that $$\left | \dfrac{\mathrm{z}-a}{z+a} \right |=1({\rm Im} (a) = 0)$$ is

lf $$\displaystyle \log_{(\frac{1}{3})}|z+1|>\log_{(\frac{1}{3})}|z-1|$$, then

$$ \left | \displaystyle \frac{1}{(1-i)^{2}}-\frac{1}{(1+i)^{2}}\right |=$$

Number of solutions of the equation $$|z|^{2}+7{z}=0$$ is

lf $$\displaystyle \log_{\sqrt{3}}\frac{|z^{2}|-|z|+1}{2+|z|}<2$$, then locus of $${z}$$ is

lf $$Z_{1},Z_{2}$$ are two unimodular Complex numbers then $$ \left |\displaystyle \frac{1}{Z_{1}}+\frac{1}{Z_{2}} \right|=$$