Number Theory T...

Which of the following statement is true?

$$i^n + i^{n + 1} + i^{n + 2}+ i^{n + 3} (n   \in   N) $$ is equal to

The number $$10$$ has four factors: $$1,2, 5$$ and $$10$$. The table below lists the number of factors for some numbers

The modulus of (1 + i) (1 + 2i) (1 + 3i) is equal to

If $$z_1, z_2, \varepsilon C$$ are such that $$|z_1 + z_2|^2 = |z_1|^2 + |z_2|^2$$ then $$\displaystyle \frac{z_1}{z_2}$$ is

The value of $$(x - 1) \displaystyle \left ( x + \frac{1}{2} - \frac{\sqrt{3}}{2} i \right )\left ( x + \frac{1}{2} + \frac{\sqrt 3}{2} i \right )$$ is

If z = x + iy and |z 1 + 2i | = | z + 1 2i |,then the locus of z is

Modulus of $$\displaystyle \frac{cos \theta- isin\theta }{sin\theta - icos\theta} is$$

If $$z_1$$ and $$z_2$$ are any two complex numbers, then $$\displaystyle \frac{z_2 + z_1}{||z_2| - |z_1||}$$ is

Number of complex numbers $$z$$ satisfying $$\left| 2z \right| =\left| 2z-1 \right| =\left| 2z+1 \right| $$ is equal to-