D.P. GUPTA, Preetima Bajpai and, Sanjeev Kumar Jha Solutions for Chapter: Complex Numbers, Exercise 2: Exercise 2

If $\left|z\right|<4,$ then $\left|iz+3-4i\right|$ is less than

If the complex number $z$ lies on a circle with centre at the origin and radius $\frac{1}{4},$ then the complex number $-1+8z$ lies on a circle with radius

The locus of a point in the Argand plane that moves satisfying the equation $\left|\left|z-1+i\right|-\left|z-2-i\right|\right|=3$ 

If $\alpha , \beta$ are the roots of the equation $t^2-2t+2=0,$ a value of $x\in R$ so that $\frac{(x+\alpha {)}^n-(x+\beta {)}^n}{\alpha -\beta }=\frac{\sin n\theta }{{\sin }^n\theta }$ is

Let $z$ and $w$ be complex numbers such that $\overline{z}+i\overline{w}=0$ and $\arg zw=\mathrm{\pi }$. Then $\arg z$ equals

If $a=\cos 2\alpha +i\sin 2\alpha , b=\cos 2\beta +i\sin 2\beta , c=\cos 2\gamma +i\sin 2\gamma$ and $d=\cos 2\delta +i\sin 2\delta \mathit{,}$ then $\sqrt{abcd}+\frac{1}{\sqrt{abcd}}=$

If $\left|\begin{array}{ccc}6i& -3i& 1\\ 4& 3i& -1\\ 20& 3& i\end{array}\right|=x+iy,$ then

If $z^2+z+1=0,$ where $z$ is complex number, then the value of ${\left(z+\frac{1}{z}\right)}^2+{\left(z^2+\frac{1}{z^2}\right)}^2+{\left(z^3+\frac{1}{z^3}\right)}^2+\dots \dots +{\left(z^6+\frac{1}{z^6}\right)}^2$ is