Number Theory T...

If $$\left| {z + 2 - i} \right| = 5$$ then the maximum value of $$\left| {3z + 9 - 7i} \right|$$ is 

Let $$A = \left\{ {z \in c:\left| z \right|} \right. = 2\left. 5 \right\}$$ and $$B = \left\{ {z \in c:\left| {z + 5 + 12i} \right|} \right. = 4$$. Then the minimum value of $$\left| {z - w} \right|$$ for $$Z \in A$$ and $$\omega  \in B$$ is :

Solve $$i^{57}+\dfrac{1}{i^{125}}$$

If $${z_1}$$ and $${z_2}$$ be complex numbers such that $${z_1} \ne {z_2}$$ and $$\left| {{z_1}} \right| = \left| {{z_2}} \right|$$. If $${z_1}$$ has positive real part and $${z_2}$$ has negative imarinary part, then $$\frac{{\left( {{z_1} + {z_2}} \right)}}{{\left( {{z_1} - {z_2}} \right)}}$$ may be

If $$|z_{1}+z_{2}|=|z_{1}-z_{2}|$$, then the different in the amplitudes of $$z_{1}$$ and $$z_{2}$$ is

The value of $$2x^{4}+5x^{3}+7x^{2}-x+41$$, when $$x=-2-\sqrt{3i}$$ is:

If the six solutions of $$x^6 = -64$$ are written in the form $$a + bi$$, where $$a$$ and $$b$$ are real, then the product those solution with $$a < 0$$, is

The value of the sum $$\displaystyle\sum^{13}_{n=1}\left(i^n+i^{n+1}\right)$$, where $$i=\sqrt{-1}$$, is?

If $$z_{1} and z_{2} are on straight line$$ $$\left| \frac { 1 } { 2 } \left( z _ { 1 } + z _ { 2 } \right) + \sqrt { z _ { 1 } z _ { 2 } } \right| + \left| \frac { 1 } { 2 } \left( z _ { 1 } + z _ { 2 } \right) - \sqrt { z _ { 1 } z _ { 2 } } \right| =$$

If $$z_{1}$$ and $$z_{2}$$ two non-zero complex number such that $$|z_{1}+z_{2}|=|z_{1}|+|z_{2}|$$, then $$arg z_{1}-arg z_{2}$$ is equal to