Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Solve this problem - Complex numbers and quadratic equations - JEE Main-7

Euler's form of z= \frac{1-7i}{\left (2+i \right )^{2}}  will be z=

  • Option 1)

    \sqrt{2}e^{i\frac{\pi }{2}}

  • Option 2)

    \sqrt{2}e^{-i\left (\frac{3\pi }{4} \right )}

  • Option 3)

    \sqrt{2}e^{i\pi}

  • Option 4)

    \sqrt{2}e^{i\frac{\pi }{4}}

 

Answers (1)

best_answer

Z=\frac{1-7i}{\left ( 2+i \right )^{2}}= \frac{1-7i}{4-1+4i}= \frac{1-7i}{3+4i}\times \frac{3-4i}{3-4i}= \frac{3-28-25i}{25}

\therefore z=-1-i

\therefore r=\left | z \right |=\sqrt{1+i}=\sqrt{2}  and arg(z) = \tan ^{-1}\left | \frac{-1}{-1} \right |-\pi

r= \sqrt2 and arg(z) \frac{-3\pi }{4}\Rightarrow z= \sqrt{2}e^{-i\frac{3\pi }{4}}

 

Euler's Form of a Complex number -

z=re^{i\theta}

- wherein

r denotes modulus of z and \theta denotes argument of z.

 

 


Option 1)

\sqrt{2}e^{i\frac{\pi }{2}}

This is incorrect

Option 2)

\sqrt{2}e^{-i\left (\frac{3\pi }{4} \right )}

This is correct

Option 3)

\sqrt{2}e^{i\pi}

This is incorrect

Option 4)

\sqrt{2}e^{i\frac{\pi }{4}}

This is incorrect

Posted by

prateek

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026: IIT Roorkee’s ECE emerges as top choice after CSE; closing rank rises
anam-khan

JEE Main 2026 application correction begins on jeemain.nta.nic.in; edit details by December 2
anam-khan

JEE Mains 2026 LIVE: NTA to conduct session 1 from January 21 to 30; exam pattern, syllabus

Latest Question