Question

If $z=x+iy$ and $x^2+y^2=16$, then the range of $\mid |x\mid -\mid y|\mid$ is

• A. [0, 4]
• B. [0, 2]
• C. [2, 4]
• D. None of these

Answer 1

The correct option is A [0, 4]

Here $x=4\cos \theta ,y=4\sin \theta$.
$\therefore ||x|-|y||=|4|cos\theta |-4|\sin \theta ||$
$=4|\parallel cos\theta |-|\sin \theta ||$
$=4\sqrt{1-2|\cos \theta ||\sin \theta |}$
$=4\sqrt{1-|\sin 2\theta |}$
Hence, the range is [0, 4]