JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

The principal value of the

\arg (z)

and

|z|

of the complex number

z=\frac{(1+\cos \theta+i \sin \theta)^5}{(\cos \theta+i \sin \theta)^3}

are

View answer and explanation

Correct option: A

-\frac{\theta}{2}, 32 \cos ^5 \frac{\theta}{2}

Option A (-

\frac{{\theta}}{{2}}

32 \cos ^5 \frac{{\theta}}{{2}}

) is correct because after simplifying using trigonometric identities and De Moivre's theorem, the argument and modulus are -

\frac{{\theta}}{{2}}

and

32 \cos ^5 \frac{{\theta}}{{2}}

, respectively.

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{\left| {1 - i} \right|^x} = {2^x}

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z \neq \pm 1

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\left|\sum\limits_{r=1}^n z_r\right|

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\alpha, \beta

\gamma

|\alpha-\beta|

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z \in C

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