Complex Numbers Questions (654)

Find the principal argument of the complex number \(\sin\dfrac{6\pi}{5} + i\left(1+\cos\dfrac{6\pi}{5}\right)\).

Number of complex numbers satisfying the equation $z^2 = \bar{z}\cdot 2^{1-k}$ is

Let $A=\{z\in\mathbb{C}:1\le|z-(1+i)|\le 2\}$ and $B=\{z\in A:|z-(1-i)|=1\}$. Then $B$:

Given that $\alpha\bar{z}+\bar{\alpha}z+\gamma=0$ is equation of a line where $\gamma$ is purely imaginary. If $\alpha^2-\beta^2=2$, where $\text{Re}(\alpha)$ and $\text{Im}(\alpha)$ are whole numbers, then slope of the line is