Complex Numbers...

If $$a, b, c$$ are real distinct numbers satisfying the condition $$a + b + c = 0$$, then the roots of the quadratic equation $$3ax^2 + 5bx + 7c = 0$$ are

Dividing $$ f(z) $$ by $$ z - i$$ we obtain the remainder i and dividing it by $$ z + i$$ we get the remainder $$1 + i$$ then remainder upon the division of $$ f(z)$$ by $$ z^{2} + 1$$ is

If the equation $$ \displaystyle 4x^{2}+x\left ( p+1 \right )+1=0 $$  has exactly two equal roots , then one of the value of $$p$$ is

If $$(\sqrt 3-i)^n=2^n, n\in N$$, then $$n$$ is a multiple of

The set of all real values of $$p$$ for which the equation $$x + 1 = \displaystyle \sqrt{px}$$ has exactly one root is

Given that $$i = \sqrt {-1}$$, find the multiplicative inverse of $$5 - i$$.

If $$(cos\theta+i\, sin \theta)\,\,( cos\,2\theta+i\,sin\,\theta)$$ ....
$$(cos\, n\theta +i\,sin\,n\theta) = 1$$, then the value of $$\theta$$ is

What is the product of the complex numbers $$\left( -3i+4 \right) $$ and $$\left( 3i+4 \right) $$?