JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

Let complex number

z=(a+\cos \theta)+(2 a-\sin \theta) i

. If

|z| \leq 2

for any

\theta \in R

, then the range of

a

View answer and explanation

Correct option: B

\left[-\frac{1}{\sqrt{5}}, \frac{1}{\sqrt{5}}\right]

Option B (

\left[-\frac{1}{\sqrt{5}}, \frac{1}{\sqrt{5}}\right]

) is correct because it represents the range of 'a' for which the magnitude of the complex number is less than or equal to 2 for all values of

\theta

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