Complex Numbers...

Nature of the roots of the quadratic equation $$2x^{2}-2\sqrt{6}x+3=0$$ is:

Find the value of $$x$$ of the equation $${ \left( 1-i \right)  }^{ x }={ 2 }^{ x }$$ 

If the discriminant of a quadratic equation is negative, then its roots are:

For what value of 'm', the equation $$(3m+1)x^{2}+2(m+1)x+m=0$$ have equal root ?

The roots of $$4x^{2}-2x+8=0$$ are:

Evaluate :

Determine the values of $$p$$ for which the quadratic equation $$2x^2 + px + 8 = 0$$ has equal roots.

$$\displaystyle \frac{\displaystyle i^{4n + 3} + (-i)^{8n - 3}}{\displaystyle(i)^{12 n- 1} - i^{2 - 16 n}}, n    \varepsilon N$$ is equal to

1+$$i^2 + i^4 + i^6 + ........+ i^{2n}$$ is

If $$i^2 = - 1$$, then the value of $$\displaystyle \sum^{200}_{n = 1} i^n $$ is