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Question

If z=x+iy and x2+y2=16, then the range of |x||y| is


Correct Answer
A
[0,4]
Your Answer
B
[0,2]
Your Answer
C
[2,4]
Your Answer
D
None of these

Solution

The correct option is A [0,4]
Here, x=cosθ, y=sinθ
|x||y|=4|cosθ|4|sinθ|
                =4|cosθ||sinθ|
                =412|cosθ||sinθ|
                =41|sin2θ|
Hence, the range is [0,4]

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