If - 1 + - 3 = r e^ i ,then is equal to - Vidyadip

MCQ

If $ - 1 + \sqrt { - 3} = r{e^{i\theta }},$then $\theta $ is equal to

A
$\frac{\pi }{3}$
B
$ - \frac{\pi }{3}$
✓
$\frac{{2\pi }}{3}$
D
$ - \frac{{2\pi }}{3}$

✓

Answer

Correct option: C.

$\frac{{2\pi }}{3}$

c
(c) Here $ - 1 + \sqrt { - 3} = r{e^{i\theta }}$==> $ - 1 + i\sqrt 3 = r{e^{i\theta }}$
$ = r\cos \theta + ir\sin \theta $
Equating real and imaginary parts, we get
$r\cos \theta = - 1$and $r\sin \theta = \sqrt 3 $
Hence$\tan \theta = - \sqrt 3 \,\, \Rightarrow \tan \theta = \tan \frac{{2\pi }}{3}$.Hence $\theta = \frac{{2\pi }}{3}$.

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

Let $\left\langle a _{ n }\right\rangle$ be a sequence such that $a_1+a_2+\ldots+a_n=\frac{n^2+3 n}{(n+1)(n+2)}$. If $28 \sum \limits_{ k =1}^{10} \frac{1}{ a _{ k }}= p _1 p _2 p _3 \ldots p _{ m }$, where $p _1, p _2, \ldots . pm$ are the first $m$ prime numbers, then $m$ is equal to

The centre of $14{x^2} - 4xy + 11{y^2} - 44x - 58y + 71 = 0$

The perpendicular distance from the point (3, -4) to the line 3x - 4y + 10 = 0:

The sides $AB,BC,CD$ and $DA$ of a quadrilateral are $x + 2y = 3,\,x = 1,$ $x - 3y = 4,\,$ $\,5x + y + 12 = 0$ respectively. The angle between diagonals $AC$ and $BD$ is ......$^o$

Which of the following statements is the inverse of "If you do not understand geometry, then you do not know how to reason deductively."?

$\tan 15^\circ = $

The locus of a point $P (h, k)$ such that the line $y = hx + k$ is tangent to $4x^2 - 3y^2 = 1$ , is a/an

Let the tangent to the parabola $y^2=12 x$ at the point $(3, \alpha)$ be perpendicular to the line $2 x+2 y=3$.Then the square of distance of the point $(6,-4)$from the normal to the hyperbola $\alpha^2 x^2-9 y^2=9 \alpha^2$at its point $(\alpha-1, \alpha+2)$ is equal to $........$.

We are to form different words with the letters of the word $INTEGER$. Let ${m_1}$ be the number of words in which $I$ and $N$ are never together and ${m_2}$ be the number of words which begin with $I$ and end with $R$, then ${m_1}/{m_2}$ is equal to

A point $P$ moves so that its distance from the point $(a,0)$ is always equal to its distance from the line $x + a = 0$. The locus of the point is