Polar form of z=4+4 3 i is - Vidyadip

MCQ

Polar form of $z=4+4 \sqrt{3} i$ is

✓
$8\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)$
B
$4\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right)$
C
$8\left(\cos \frac{5 \pi}{3}+i \sin \frac{5 \pi}{3}\right)$
D
$4\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)$

✓

Answer

Correct option: A.

$8\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)$

(A)
$z =4+4 \sqrt{3} i$
$|z|=\sqrt{4^2+(4 \sqrt{3})^2}=8$
Also, $a=4$ and $b=4 \sqrt{3}$
$\therefore \quad \theta=\tan ^{-1}\left(\frac{4 \sqrt{3}}{4}\right)=\tan ^{-1}(\sqrt{3})=\frac{\pi}{3}$
Polar form of $z=|z|(\cos \theta+i \sin \theta)$
$=8\left(\cos \frac{\pi}{3}+ i \sin \frac{\pi}{3}\right)$

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

If the number of elements in the sets G and A are 3 and 4 respectively, then match the items of List I with those of List II.

	List I		List II
(a)	The number of non bijective functions from GG to G	I.	24
(b)	The number of bijective functions from A to A	II.	0
(c)	The number of functions from G to GA	III.	1728
(d)	The number of surjective functions from A to AA	IV.	12
		V.	19683

The line passing through (1, 0) and (- 2, $\sqrt{3}$) makes an angle of _________ with X-axis

The two numbers such that each one is square of the other are

In a $G.P.$ if the $(m + n)^{th}$ terms is $p$ and $(m - n)^{th}$ term is $q,$ then its $m^{th}$ term is:

The probability that a student knows the correct answer to a multiple-choice question is

$\frac{2}{3}$. If the student does not know the answer, then the student guesses the answer. Theprobability of the guessed answer being correct is $\frac{1}{4}$. Given that the student has answered

the question correctly, the probability that the student knows the correct answer is

The equation of locus of a point, such that sum of its distance from points (2, 0) and (-2, 0) is 6, is

If $A=\left[\begin{array}{ll}\alpha & 2 \\ 2 & \alpha\end{array}\right]$ and $\left|\mathrm{A}^3\right|=125$, then $\alpha=$

The equation of the tangent to the ellipse $2 x^2+3 y^2=30$ at the point $(-3,2)$ is

$\tan 20^{\circ} \tan 40^{\circ} \tan 60^{\circ} \tan 80^{\circ}=$

$\begin{array}{rlrl}\text {If } f(x) & =\frac{\log x-\log 7}{x-7}, & x \neq 7 \\& =k ,& x=7\end{array}$
is continuous at $x=7$, then the value of $k$ is