JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

Let

z_1

and

z_2

be given by

z_1=\left(\frac{2+i \sqrt{5}}{2-i \sqrt{5}}\right)^{10} \text { and } z_2=\left(\frac{2-i \sqrt{5}}{2+i \sqrt{5}}\right)^{10}

Then

\left|z_1+z_2\right|

is equal to

View answer and explanation

Correct option: A

2 \cos \left(20 \cos ^{-1} \frac{2}{3}\right)

Option C (

2 \cos \left(10 \cos ^{-1} \frac{2}{3}\right)

) is correct because by converting to polar form and using De Moivre's theorem, the expression simplifies to this result.

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