A particle P starts from the point $\mathrm{Z}_0=1+2 \mathrm{i}$ where $\mathrm{i}=\sqrt{-1}$. It moves first horizontally away from the origin by 5 units and then vertically upwards parallel to positive Y -axis by 3 units to reach a point $Z_1$. From $Z_1$ the particle moves $\sqrt{2}$ units in the direction of vector $\hat{\mathrm{i}}+\hat{\mathrm{j}}$ and then it moves through an angle $\frac{\pi}{2}$ in anticlockwise direction on a circle with centre at origin to reach at point $Z_2$, then $Z_2=$

Let $z$ be the complex number with $\operatorname{Im}(z)=10$ and satisfying $\frac{2 \mathrm{z}-\mathrm{n}}{2 \mathrm{z}+\mathrm{n}}=2 \mathrm{i}-1$, where $\mathrm{i}=\sqrt{-1}$, for some natural number ' $n$ ' then

Argument of the complex number $z=\frac{13-5 i}{4-9 i}, i=\sqrt{-1}$ is

If $x=-2+\sqrt{-3}$, then the value of $2 x^4+5 x^3+7 x^2-x+38$ is equal to