Search Colleges, Exams, Schools & more
Login
Polar form of complex numbers - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
-
13 Questions around this concept.
Solve by difficulty
EASYCorrect result for $\left ( 4+4\sqrt{3}\:\: i \right )^{\frac{4}{5}}$ is :
What is the polar term of $z=-4+4 i$ ?
Concepts Covered - 1
Polar form of complex numbers
In polar form, we represent the complex number through the argument and modulus value of complex numbers.
Let $z=x+i y$ be a complex number,
And we know that
$|z|=\sqrt{x^2+y^2}=r$
And let arg(z) = θ
From the figure, $x=|z| \cos (\theta)=r \cos (\theta)$
and $y=|z| \sin (\theta)=r \sin (\theta)$
So, $z=x+i y=r \cos (\theta)+i . r \sin (\theta)=r(\cos (\theta)+i . \sin (\theta))$
This form is called polar form with $r=$ principal value of $\arg (z)$ and $r=|z| . \mid$
For general values of the argument
$\mathrm{z}=\mathrm{r}[\cos (2 \mathrm{n} \pi+\theta)+i \sin (2 \mathrm{n} \pi+\theta)]$, where $n \in$ Integer
Study it with Videos
"Stay in the loop. Receive exam news, study resources, and expert advice!"
Get Answer to all your questions
B.Tech/B.Arch Admissions OPEN
Among top 100 Universities Globally in the Times Higher Education (THE) Interdisciplinary Science Rankings 2026
UPES B.Tech Admissions 2026
ApplyLast Date to Apply Extended till Today, 30th April | Ranked #43 among Engineering colleges in India by NIRF | Highest Package 1.3 CR , 100% Placements
Amrita University B.Tech 2026
ApplyRecognized as Institute of Eminence by Govt. of India | NAAC ‘A++’ Grade | Upto 75% Scholarships
MAHE, Manipal - B.Tech Admissions 2026
ApplyExtended Application Deadline: 30th April | NAAC A++ Accredited | NIRF Rank #3
Reva University B.Tech Admissions 2026
ApplyQS I-Gauge Diamond Rated | NAAC A+ Accredited | 621 Recruitment Partners | INR 40 LPA Highest CTC | 4482 Job offers
Manav Rachna-B.Tech Admissions 2026
ApplyNAAC A++ Grade | Recognized as Category-1 Deemed to be University by UGC | 41,000 + Alumni Imprints Globally