No Author Solutions for Exercise 1: EXERCISE

The vertices $B$ and $D$ of a parallelogram are $1-2i$ and $4+2i.$ If the diagonals are at right angles and $AC=2BD,$ then the complex number representing $A$ is

$z_1$ and $z_2$ are unimodular complex number that satisfy $z_1^2+z_2^2=4$, then ${\left(z_1+{\overline{z}}_1\right)}^2+{\left(z_2+{\overline{z}}_2\right)}^2$ is equal to

The complex number $z$ satisfying $|z+\overline{z}|+|z-\overline{z}|=2$ and $|iz-1|+|z-i|=2$ is/are

The number of real solutions of the equation $\left|x^2+4x+3\right|+2x+5=0$ are

The equation $\left(\cos \beta -1\right)x^2+\left(\cos \beta \right)x+\sin \beta =0$ in the variable $x$ has real roots, then $\beta$ is in the interval.

If $x^2+5=2x-4\cos \left(a+b\right)$, where $a, b\in \left(0, 5\right)$, is satisfied for atleast one real $x,$ then the maximum value of $a+b$ in $\left[0, 2\pi \right]$

The set of value of $\text{'}a\text{'}$ for which $1$ lies between the roots of equation $x^2-ax-a+3=0$ is

The value of $\left|a\right|$ for which $\sin \theta$ and $\mathrm{cosec}\theta$ are the roots of the equation $x^2+ax+b=0$ is