For a positive integer n, the expression (1- i )^ n (1-1 i )^ n e… - Vidyadip

MCQ

For a positive integer $n$, the expression $(1- i )^{ n }\left(1-\frac{1}{ i }\right)^{ n }$ equals

A
$0$
B
$2 i ^{ n }$
✓
$2^n$
D
$4^n$

✓

Answer

Correct option: C.

$2^n$

(C)
$(1- i )^{ n }\left(1-\frac{1}{ i }\right)^{ n }=(1- i )^{ n }\left(\frac{ i -1}{ i }\right)^{ n }$
$=\left[(1-i)^2\right]^n\left(\frac{-1}{i}\right)^n$
$=\left(1+ i ^2-2 i \right)^{ n }\left(\frac{ i ^2}{ i }\right)^{ n }$
$=(1-1-2 i )^{ n }( i )^{ n }$
$=(-2 i )^{ n }( i )^{ n }$
$=\left(-2 i^2\right)^n$
$=2^n$

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 Complex Numbers→Complex Numbers — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

The tenth term of the geometric sequence is $\frac{1}{4}, \frac{-1}{2}, 1,-2, \ldots$ is

If $\sqrt{3}\cos\text{x}+\sin\text{x}=\sqrt{2},$ then general value of $\theta$ is :

If $\cot\text{x}-\tan\text{x}=\sec\text{x},$ then $,x$ is equal to :

Let $\text{A} = \{\text{x : x} \in \text{R}, \text{x > 4}\}$ and $\text{B}= \{\text{x}\in\text{R : x} < 5\}.$ Then, $\text{A}\cap\text{B}=$

If the roots of $x^2− bx + c = 0$ are two consecutive integers, then $b^2 − 4 c$ is:

If $\frac{3+i \sin \theta}{4-i \cos \theta}, \theta \in[0,2 \pi]$, is a real number, then an argument of $\sin \theta+ i \cos \theta$ is

If $Z_1=4 i^{40}-5 i^{35}+6 i^{17}+2, Z_2=-1+i$, where $i=\sqrt{-1}$, then $\left|Z_1+Z_2\right|=$

If A(- 5, 2) and B(- 1, 5) are two points, then the equation of perpendicular bisector of segment AB is

If $p, q$ be two $A.M.'s$ and $G$ be one $G.M. $ between two numbers, then $G^2 =$

Sum to infinity of a G.P. $5,-\frac{5}{2}, \frac{5}{4},-\frac{5}{8}, \frac{5}{16}, \ldots$ is