If n is a positive integer greater than unity and z is a complex … - Vidyadip

MCQ

If $n$ is a positive integer greater than unity and $z$ is a complex number satisfying the equation ${{z}^{n}}={{(z+1)}^{n}}$, then

✓
$\operatorname{Re}(z)<0$
B
$\operatorname{Re}(z)>0$
C
$\operatorname{Re}(z)=0$
D
None of these

✓

Answer

Correct option: A.

$\operatorname{Re}(z)<0$

A

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 "M.C.Q (1 Marks)" from Complex Numbers→Complex Numbers — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The radius of the circle passing through the point $(6, 2)$ and two of whose diameters are $x + y = 6$and $x + 2y = 4$ is

In an isosceles trapezium, the length of one of the parallel sides, and the lengths of the non-parallel sides are all equal to $30$ . In order to maximise the area of the trapezium, the smallest angle should be

Locus of the centre of the circle touching both the co-ordinates axes is

The mean age of a combined group of men and women is $30$ years. If the means of the age of men and women are respectively $32$ and $27$, then the percentage of women in the group is

If the $1011^{\text {th }}$ term from the end in the binomial expansion of $\left(\frac{4 x}{5}-\frac{5}{2 x }\right)^{2022}$ is 1024 times $1011^{\text {th }}$ term from the beginning, then $|x|$ is equal to

A point $P$ is taken outside $\Delta ABC$ where $(B(1, \sqrt 3 ), A(0, 0)$ and $C(2, 0))$ , but inside the acute angle $BAC$ , such that $\angle APC = \frac{\pi }{6}$ and $\angle BPA = \frac{\pi }{{12}}$ . Slope of the line $BP$ is

The value of $\mathop \sum \limits_{k = 1}^{10} \left( {\sin \frac{{2k\pi }}{{11}} + i\cos \frac{{2k\pi }}{{11}}} \right)$ is

If $f(x) = ax + b$ and $g(x) = cx + d$ and $f{g(x)} = g{f(x)}$ then:

If ${{x}_{r}}=\cos \left( \frac{\pi }{{{2}^{r}}} \right)+i\sin \left( \frac{\pi }{{{2}^{r}}} \right)$, then${{x}_{1}}.{{x}_{2}}......\infty $is [RPET 1990, 2000; BIT Mesra 1996; Karnataka CET 2000]

Let $w=\frac{\sqrt{3}+i}{2}$ and $P=\left\{w^n: n=1,2,3, \ldots\right\}$. Further $H_1=\left\{z \in C: \operatorname{Re} z>\frac{1}{2}\right\}$ and $H_2=\left\{z \in C: \operatorname{Re} z<-\frac{1}{2}\right\}$. where $C$ is the set of all complex numbers. If $z_1 \in P \cap H_1, z_2 \in P \cap H_2$ and $O$ represents the origin, then $\angle z _1 O z _2=$

$(A)$ $\frac{\pi}{2}$ $(B)$ $\frac{\pi}{6}$ $(C)$ $\frac{2 \pi}{3}$ $(D)$ $\frac{5 \pi}{6}$