Complex Numbers...

If $$\alpha $$ and $$\beta $$ are real then $$\left| \dfrac { \alpha +i\beta  }{ \beta +i\alpha  }  \right|=$$ 

If $$m_1$$, $$m_2$$, $$m_3$$ and $$m_4$$ respectively denote the moduli of the complex numbers $$1 + 4i, 3 + i, 1 – i \ and\  2 – 3i$$ then the correct order among the following is :

The principal argument of $$z=-3+3i$$ is:

Assertion (A): The principal amplitude of complex number $$x + ix$$ is $$\cfrac{\pi }{4}$$.
Reason (R): The principal amplitude of a complex number $$x + iy$$ is $$\cfrac{\pi }{4}$$ if $$y = x$$.

The area of the triangle formed by the three complex numbers $$1 + i$$, $$i - 1$$ , $$2i$$ in the Argand diagram is:

If $$z_1$$ and $$z_2$$ are two complex numbers, then $$Re(z_1z_2)$$ is:

In the argand diagram, the complex number z is in the fourth quadrant,  then $$\overline{z}$$, $$-z$$, $$\overline{-z}$$ are respectively are in quardrants

The value of $$1+(1+i)+(1+i)^2+(1+i)^3=$$

lf $$(x+iy)(2+cos\theta+isin\theta)=3$$ then $$x^{2}+y^{2}-4x+3$$ is

If $$z_1$$, $$z_2$$ are the complex numbers such that $$|z_1+z_2|=|z_1|+|z_2|$$ then arg $$z_1 - $$ arg $$z_2$$ is