List of top Mathematics Questions on Complex Numbers and Quadratic Equations asked in AP EAPCET

If \[ z=\frac{(1-i)^3}{(\sqrt{3}-i)^2}, \] then the complex conjugate of \(z\) is:

The locus of the point \(z=x+iy\) satisfying \[ \left|\frac{z-(2+i)}{z+(2-i)}\right|=2 \] is:

If $\omega$ is a complex cube root of unity, then $(1 - \omega + \omega^2)^5 + (1 + \omega - \omega^2)^5 =$

If $z = \frac{\sqrt{3} + i}{2}$, then $z^{101} + z^{103} =$

If the roots of the quadratic equation $x^2 - 2px + q^2 = 0$ are real and distinct, then:

If $\alpha, \beta$ are the roots of the quadratic equation $x^2 - 2x + 4 = 0$, then the value of $\alpha^n + \beta^n$ is:

If \[ x=-5+2\sqrt{-4}, \] then the value of \[ x^4+9x^3+35x^2-x+4 \] is:

Multiplicative inverse of the complex number \[ (\sin\theta,\cos\theta) \] is

If \(\alpha,\beta\) are the roots of the equation \[ 2x^2+6x+k=0, \] then the maximum value of \[ \frac{\alpha}{\beta}+\frac{\beta}{\alpha} \] when \(k<0\) is:

If \[ |z-3i|+|z+5i|=4, \] then the locus of \(z\) is:

If \[ (x-iy)^{\frac{1}{3}}=2-i\sqrt{3} \] and the point \(z=(x,y)\) lies on the line \[ \frac{x}{2}+\frac{y}{\sqrt{3}}=k, \] then \(k=\)

If \[ \left|z+\frac{2}{z}\right|=2, \] then the maximum value of \(|z|\) is:

A complex number \(z\) among the following which does not satisfy \[ z^3+27i=0 \] is: