JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

k

non-overlapping regular polygons of

p_1, p_2, \ldots, p_k

sides have one common vertex so that no gap is left at that vertex. Then

\frac{1}{p_1}+\frac{1}{p_2}+\cdots+\frac{1}{p_k}

is equal to

View answer and explanation

Correct option: B

\frac{k}{2}-1

The value of

\left(\frac{{1+i \sin \frac{{\pi}}{{8}}+\cos \frac{{\pi}}{{8}}}}{{1-i \sin \frac{{\pi}}{{8}}+\cos \frac{{\pi}}{{8}}}}\right)^8

is -1 because it simplifies to -1 using trigonometric identities and De Moivre's theorem.

More Questions from COMPLEX NUMBERS

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

|z|=1

z \neq \pm 1

z, \frac{z}{1-z^2}

\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

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

(z+a b)^3=a^3

a \neq 0

\alpha, \beta

\gamma

|\alpha-\beta|

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}