List of top Mathematics Questions on Complex numbers asked in TS EAMCET

Let \(z\) be a complex number such that \(Re(z)=3\) and \(Im(z)\neq 0\). If \[ \frac{3z-n}{z+n}=\frac{5-i}{2} \] for a real number \(n\), then \(n-Im(z)= \)

If \[ \sqrt[3]{i}=cis~\alpha,\qquad \alpha \text{ belongs to second quadrant} \] and \[ \sqrt[3]{-i}=cis~\beta,\qquad \beta \text{ belongs to third quadrant} \] then \[ cis~\alpha+cis~\beta= \]

If \[ z=i^i \] then \[ z^i= \]

If \[ \sqrt{-4x+2i\sqrt{x^{4}+2x^{2}+9}} = \pm(a+ib) \] then \[ a^2+b^2-6= \]

Product of all the five values of \[ (1-i)^{4/5} \] is

If \( \omega \) is a complex cube root of unity, then \[ \cos\left(\left(\omega^{1234} + \omega^{2021}\right)\pi - \frac{\pi}{4}\right) = \]