List of top Mathematics Questions on conjugate of a complex number asked in KEAM

Evaluate \( \int \frac{x^2 + 6x + 1}{(x+3)^2} \, dx \).

Let \(z_{1} = \frac{1}{2} +i\frac{\sqrt{3}}{2}\) and \(z_{2} = -\frac{1}{2} -i\frac{\sqrt{3}}{2}\) . If \(w = z_{1} + \bar{z}_{2}\) , then \(\overline{w} =\)

If the conjugate of a complex number \( z \) is \( \frac{1}{i - 1} \), then \( z \) is

If the conjugate of a complex number \( z \) is \( \frac{1}{i - 1} \), then \( z \) is