Download App

4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
If $n$ is a positive integer, then ${\left( {\frac{{1 + i}}{{1 - i}}} \right)^{4n + 1}}$=
  • A
    $1$
  • B
    $-1$
  • ✓
    $i$
  • D
    $ - i$
✓

Answer

Correct option: C.
$i$
c
(c)Since $\frac{{1 + i}}{{1 - i}} = \frac{{(1 + i)(1 + i)}}{{(1 - i)(1 + i)}} = i$
Therefore ${\left( {\frac{{1 + i}}{{1 - i}}} \right)^{4n + 1}} = {i^{4n + 1}} = i{i^{4n}} = i\,\,\,\,\,({i^{4n}} = 1)$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 4.1 complex nubers→4.1 complex nubers — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Eight chairs are numbered $1$ to $8$. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked $1$ to $4$ and then men select the chairs from amongst the remaining. The number of possible arrangements is
→
Let $A_1$ and $A_2$ be two arithmetic means and $G_1, G_2$, $G _3$ be three geometric means of two distinct positive numbers. The $G _1^4+ G _2^4+ G _3^4+ G _1^2 G _3^2$ is equal to
→
If $\tan(\text{A}-\text{B})=1,\sec(\text{A+B})=\frac{2}{\sqrt{3}},$ then the smallest positive value of B is:
→
If $\frac{{{{(1 - 3x)}^{1/2}} + {{(1 - x)}^{5/3}}}}{{\sqrt {4 - x} }}$ is approximately equal to $a + bx$ for small values of $x$, then $(a,b)$=
→
 Remainder when $ 64^{32^{32}}$  is divided by  $9$ is equal to .........................
→
The middle term in the expansion of ${\left( {1 - \frac{1}{x}} \right)^n}\left( {1 - {x}} \right)^n$ in powers of $x$ is
→
Determine the domain and range of the relation R defined by:
$\text{R}=\{(\text{x, x,}+5):\text{x}\in\{0,1,2,3,4,5\}\}$
→
The equation of the parabola whose focus is the point $(0, 0)$ and the tangent at the vertex is $x - y + 1 = 0$ is
→
Numbers greater than $1000$ but not greater than $4000$ which can be formed with the digits $0, \,1, \,2, \,3, \,4$ (repetition of digits is allowed), are
→
Let $f:(0,1) \rightarrow \mathbb{R}$ be the functions defined as $f(x)=\sqrt{n}$ if $x \in\left[\frac{1}{n+1}, \frac{1}{n}\right)$ where $n \in N$. Let $g:(0,1) \rightarrow \mathbb{R}$ be a function such that $\int_{x^2}^x \sqrt{\frac{1-t}{t}} d t$ $ < g(x) < 2 \sqrt{x}$ for all $x \in(0,1)$. Then $\lim _{x \rightarrow 0} f(x) g(x)$
→