If $(2+i)$ is a root of the equation $x^3-5x^2+9x-5=0$,then the other roots are

For all complex numbers $z$ of the form $1 + i\alpha$,where $\alpha \in R$,if $z^2 = x + iy$,then which of the following relations holds?

If $\alpha$ denotes the number of solutions of $|1-i|^x=2^x$ and $\beta=\left(\frac{|z|}{\arg (z)}\right)$,where $z=\frac{\pi}{4}(1+i)^4\left(\frac{1-\sqrt{\pi}i}{\sqrt{\pi}+i}+\frac{\sqrt{\pi}-i}{1+\sqrt{\pi}i}\right)$,$i=\sqrt{-1}$,then the distance of the point $(\alpha, \beta)$ from the line $4x-3y=7$ is

If $-i$ and $\alpha$ are the roots of the equation $iz^2 - 2(i+1)z + (2-i) = 0$,$\tan \theta = \frac{-1}{2}$ and $\theta \in 4^{\text{th}}$ quadrant,then $5^3 \cos 6\theta =$

If $z_1 = 2 - 3i$ and the roots of the equation $z^3 + bz^2 + cz + d = 0$ are $i$,$z_1$,and $\bar{z}_1$,then $b + c + d =$

The number of solutions for $z^3+\bar{z}=0$ is