If z and w are two complex numbers such that |zw|=1 

and arg(z)-arg(w)=\frac{\pi}{2},  then : 

  • Option 1)

  • Option 2)

    z\bar w=\frac{-1+i}{\sqrt2}

  • Option 3)

    \bar z w=-i

  • Option 4)

    z\bar w=\frac{1-i}{\sqrt2}

Answers (1)

|zw|=1 and arg(z)-arg(w)=\frac{\pi}{2},

Let |z|=r   => z=re^{i\theta}

|\omega |=\frac{1}{r}    => \omega =\frac{1}{r}e^{i\phi }

arg(z)-arg(w)=\frac{\pi}{2}

\theta -\phi =\frac{\pi}{2}

\theta =\frac{\pi}{2}+\phi

z\bar{\omega }=re^{i\theta }.\frac{1}{r}e^{-i\phi }

        =re^{i(\theta -\phi)}    

        =re^{i(\frac{\pi}{2}+\phi -\phi)}

        =re^{i(\frac{\pi}{2})}

        =cos(\frac{\pi}{2})+isin(\frac{\pi}{2})

        =0+i.1

        =i

 


Option 1)

Option 2)

z\bar w=\frac{-1+i}{\sqrt2}

Option 3)

\bar z w=-i

Option 4)

z\bar w=\frac{1-i}{\sqrt2}

Preparation Products

Knockout JEE Main Sept 2020

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 12999/- ₹ 6999/-
Buy Now
Rank Booster JEE Main 2020

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 9999/- ₹ 4999/-
Buy Now
Test Series JEE Main Sept 2020

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 4999/- ₹ 1999/-
Buy Now
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions