The equation $|z+1-i|=|z-1+i|$ represents a (where z is a complex number)

If $\int \frac{2 x+3}{(x-1)\left(x^2+1\right)} d x$

$$ =\log _e\left\{(x-1)^{\frac{5}{2}}\left(x^2+1\right)^2\right\}-\frac{1}{2} \tan ^{-1} x+\mathrm{A} $$

where A is an arbitrary constant, then the value of $a$ is

The money invested in a company is compounded continuously. ₹ 400 invested today becomes ₹ 800 in 6 years, then at the end of 33 years, it will become .. $(\sqrt{2}=1.4142)$

If $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ are unit vectors and $\theta$ is the angle between them, then $\overline{\mathrm{a}}+\overline{\mathrm{b}}$ is a unit vector when $\theta$ is