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If $z = x + i y and x^{2} + y^{2} = 16$ then the range of $| | x | - | y | |$ is

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[0, 4]

[0, 2]

[2,4]

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Correct option is A

Here x=4cos⁡θ,y=4sin⁡θ∴ ∥x|−|y∣∥=|4|cos⁡θ|−4|sin⁡θ||=4||cos⁡θ|−|sin⁡θ||=41−2|cos⁡2θ||sin⁡θ|=41−|sin⁡2θ|Hence, the range is [0, 4].

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

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If $z = x + i y and x^{2} + y^{2} = 16$ then the range of $| | x | - | y | |$ is