Complex Numbers...

If the roots of the equation x² - nx + m = 0 differ by 1, then:

The quadratic equation \(7 x^{2}-28 x+21\) have roots \(\alpha\) and \(\beta\). And \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{k}{\alpha \beta}\) then find the value of \(k\).

A quadratic equation ax² + bx + c = 0 has no real roots, if:

Find the real and imaginary part of the complex number \(z =\frac{1- i }{1+ i }\).

If α and β are the roots of the equation x² - q(1 + x) - r = 0, then (1 + α)(1 + β) isequal to:

The quadratic equation \(2 x^{2}-\sqrt{5} x+1=0\) has:

The conjugate of \(\frac{(2- i )(1+2 i )}{(3+ i )(2-3 i )}\) is:

If α and β are the roots of the equation ax² + bx + c = 0, where a ≠ 0, then (aα + b) (aβ + b) is equal to:

Find the value of \(i ^{1325}\) where \(i =\sqrt{-1}\).

If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \((5+\sqrt{2}) x^{2}-(4+\sqrt{5}) x+(8+2 \sqrt{5})=0\), then the value of \(\frac{2 \alpha \beta }{(\alpha+\beta)}\) is: