Download App

STD 11 - 4.1 complex nubers — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.1 complex nubers4 Marks
Question
If $(1 - i)^n = 2^n,$ then $n = $
✓

Answer

b
(b) If $(1 - i)^n = 2^n$ ......$(i)$
We know that if two complex numbers are equal, their moduli must also be equal, therefore from $(i)$, we have
$|(1 - i)^n|\, = \,|2^n|$

$ \Rightarrow $ $|1 - i|^n = \,|2|^n$,$(\because \,\,2^n > 0)$
==> $\left[ \sqrt {{1^2} + {{( - 1)}^2}}  \right]^n = 2^n$

==> $(\sqrt 2 )^n = 2^n$
==> $2^{n/2} = 2^n$

==> $\frac{n}{2} = n$

==>$n = 0$
Trick : By inspection, ${(1 - i)^0} = {2^0}\,\,\,\, \Rightarrow 1 = 1$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The number of possible tangents which can be drawn to the curve $4x^2 - 9y^2 = 36$ , which are perpendicular to the straight line $5x + 2y -10 = 0$ is
→
Let $P ( x )$ be a real polynomial of degree $3$ which vanishes at $x =-3 .$ Let $P ( x )$ have local minima at $x=1,$ local maxima at $x=-1$ and $\int_{-1}^{1} P ( x ) d x =18,$ then the sum of all the coefficients of the polynomial $P ( x )$ is equal to ....... .
→
The sum of the common terms of the following three arithmetic progressions.

$3,7,11,15,...................,399$

$2,5,8,11,............,359$ and

$2,7,12,17,...........,197$, is equal to $................$.

→
Six ‘$+$’ and four ‘$-$’ signs are to placed in a straight line so that no two ‘$-$’ signs come together, then the total number of ways are
→
In an examination of Mathematics paper, there are $20$ questions of equal marks and the question paper is divided into three sections :$ A, B$ and $C . A$ student is required to attempt total $15$ questions taking at least $4$ questions from each section. If section $A$ has $8$ questions, section $B$ has $6$ questions and section $C$ has $6$ questions, then the total number of ways a student can select $15$ questions is $........$
→
Let $P_{1}$ be a parabola with vertex $(3,2)$ and focus $(4,4)$ and $P _{2}$ be its mirror image with respect to the line $x +2 y =6$. Then the directrix of $P _{2}$ is $x +2 y$ =
→
Let $A B C$ be an equilateral triangle, let $K L M N$ be a rectangle with $K, L$ on $B C, M$ on $A C$ and $N$ on $A B$. Suppose $A N / N B=2$ and the area of $\triangle B K N$ is $6$ .The area of the $\triangle A B C$ is
→
Let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit

$\lim _{x \rightarrow 0^{+}} \frac{(1-x)^{\frac{1}{x}}-e^{-1}}{x^a}$

is equal to a nonzero real number, is. . . . . . . 

→
Let for $A=\left[\begin{array}{lll}1 & 2 & 3 \\ a & 3 & 1 \\ 1 & 1 & 2\end{array}\right],|A|=2$. If $|2 \operatorname{adj}(2 \operatorname{adj}(2 A ))|$ $=32^{ n }$, then $3 n +\alpha$ is equal to
→
Let $h (x)$ be differentiable for all $x$ and let $f (x) = (kx + e^x) h(x)$ where $k$ is some constant. If $h (0) = 5, h ' (0) = - 2$ and $f ' (0) = 18$ then the value of $k$ is equal to
→