What is the conjugate of \( \dfrac{2 - i}{(1 - 2i)^2} \)?
-\(\dfrac{2}{25}\) − i \(\dfrac{11}{25}\)
If \(|z_1| = |z_2|\), is it necessary that \(z_1 = z_2\)?
No
If \( \dfrac{(a^2+1)^2}{2a - i} = x + iy \), what is the value of \(x^2 + y^2\)?
\( \dfrac{(a^2+1)^4}{4a^2 + 1} \)
Find \(z\) if \(|z| = 4\) and \(\arg(z) = \dfrac{5\pi}{6}\).
-2\sqrt{3} + 2i
Find \( \left| \dfrac{(1+i)(2+i)}{3+i} \right| \).
1
Find the principal argument of \((1 + i\sqrt{3})^2\).
\( \dfrac{2\pi}{3} \)
Where does \(z\) lie if \( \left| \dfrac{z - 5i}{z + 5i} \right| = 1 \)?
Real axis