Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Tell me? - Complex numbers and quadratic equations - JEE Main-14

Let   \frac{z_{1}}{z_{2}}= 3-4i  and  z_{2}= 12+5i  then \left |z_{1} \right |  equals

  • Option 1)

    \frac{13}{5}

  • Option 2)

    \frac{5}{13}

  • Option 3)

    \frac{1}{65}

  • Option 4)

    65

 

Answers (1)

best_answer

\because \left | \frac{z_{1}}{z_{2}} \right |=\frac{\left |z_{1} \right |}{\left |z_{2} \right |}\Rightarrow \left | z_{1} \right |=\left | \frac{z_{1}}{z_{2}} \right |\cdot \left | z_{2} \right |

From given, we have 

\left | \frac{z_{1}}{z_{2}} \right |=\sqrt{9+16}=5  and  \left | z_{2} \right |=\sqrt{144+25}=13

\therefore \left |z_{1} \right |=5\times 13=65

\therefore Option (D)

 

Property of Modulus of z(Complex Number) -

\left |\frac{z_{1}}{z_{2}} \right |=\frac{\left |z_{1} \right |}{\left |z_{2} \right |}

- wherein

|.| denotes modulus of complex number

 

 


Option 1)

\frac{13}{5}

This is incorrect

Option 2)

\frac{5}{13}

This is incorrect

Option 3)

\frac{1}{65}

This is incorrect

Option 4)

65

This is correct

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 Registration LIVE: NTA JEE form at jeemain.nta.nic.in; what's new this year?
anam-khan

JEE Main 2026: Wider gap in NIT cut-offs for home and other-state quotas; outsiders need better rank
anam-khan

JEE Mains 2026: Use of calculator 'not allowed’ says NTA; cites ‘typographical error' in information bulletin

Latest Question