# NDA MATHEMATICS QUIZ - 1

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## Question 1:

It $|z|=1$ then the quantity $\frac{z}{1+z^{2}}$ is

## Question 2:

Locus of a point $z$, which moves in a such a way that $|z-3|=5$, represents a:

## Question 3:

Square root of $(8-15 i)$ will be

## Question 4:

If. $\omega$ be the complex cube root of unity then the value of $\left(\frac{1}{\omega^{2}}-\frac{1}{\omega}+1\right)^{7}$ is:

## Question 5:

$\left(\frac{1-i}{1+i}\right)^{300}+\left(\frac{1+i}{1-i}\right)^{102}$ is equal to:

## Question 6:

It $n$ is an interger then amplitude $z=\frac{(i +\sqrt{3})^{8 n+5}}{(1-i \sqrt{3})^{8 n+4}}$ is:

## Question 7:

If $7-\sqrt{2} i$ is a root of the equation $x^{2}-2 lx+m$ $=0$ then the values of $l$ and $m$ will be given as

## Question 8:

$\frac{(1+i)^{3}}{4+3 i}$ is eqivalent to:

## Question 9:

Value of $\left\{i^{21}+\left(\frac{1}{i}\right)^{27}\right\}^{2}$ is:

## Question 10:

It $i^{2}=-1$ then the value of $i^{(1+2+3+\ldots \ldots+\mathrm{n})}$will be (Where n$\in$I)