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  • Help me understand! - Complex numbers and quadratic equations - JEE Main-16

Euler's form of z= \sqrt{3}-i is z=

  • Option 1)

    1e^{-i\frac{\pi }{6}}

  • Option 2)

    2e^{i\frac{\pi }{6}}

  • Option 3)

    1e^{i5\frac{\pi }{6}}

  • Option 4)

    2e^{-i\frac{\pi }{6}}

 

Answers (1)

best_answer

\because z= \sqrt{3}+i

\therefore r= \left | z \right | = {\sqrt{3+1}}=2

and Z being in 4th quadrant , its arg(z) will be : 

-\tan^{-1}\left | \frac{-1}{\sqrt{3}} \right |= \frac{-\pi }{6}

Z = 2e^{-i\frac{\pi }{6}}

 

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)

1e^{-i\frac{\pi }{6}}

This is incorrect

Option 2)

2e^{i\frac{\pi }{6}}

This is incorrect

Option 3)

1e^{i5\frac{\pi }{6}}

This is incorrect

Option 4)

2e^{-i\frac{\pi }{6}}

This is correct

Posted by

Aadil

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