Number Theory T...

If $$z = x + iy$$ and $$x^2 + y^2 = 16$$, then the range of $$\left|\left|x\right| - \left|y\right|\right|$$ is 

If $$\displaystyle z_1\neq -z_2$$ and $$\displaystyle |z_1+z_2|=\left| \frac{1}{z_1}+\frac{1}{z_2}\right| $$ then

The complex number z satisfies the condition $$\displaystyle \left | z- \frac{25}{z} \right | = 24$$. The maximum distance from the origin of co-ordinates to the point z is

The roots of the equation $$z^n = (z + 1)^n$$ on the complex plane lie on the line

If $$\left|z\right |^2 - 3 = 3\left|z\right|$$, then the value of $$\left|z\right|$$ is

Find the complex numbers z which simultaneously satisfy the equation $$\displaystyle \left | \frac{z - 12}{z - 8 i} \right | = \frac{5}{3}$$ and $$\displaystyle \left | \frac{z - 4}{z - 8} \right | = 1$$.

If $$z$$ is a complex number such that $$-\pi / 2 \le$$ arg $$ z \le \pi / 2,$$ then which of the following inequality is true? 

If $$i{ z }^{ 3 }+{ z }^{ 2 }-z+i=0$$, then 

Locate the complex number $$z = x + iy$$ for which $$log_{1/3} \{ log_{1/2} (|z|^2 + 4 |z| + 3) \} < 0$$

Number of roots of the equation $$z^{10} - z^5 - 992 = 0$$ where real parts are negative is