Q If z=z+iy and x2+y2 = 16, then what is the range of ||x-|-|y|| - Maths - Relations and Functions

Question

Q If z=z+iy and x 2 + y 2 = 16, then what is the range of
||x-|-|y||?

Shruti Tyagi · Accepted Answer

Dear student,

Let x=4cosθ and y=4sinθ then,putting the value inx-y =4cosθ-4sinθ=4cosθ-sinθ=4cosθ-sinθ2=4cos2θ+sin2θ-2cosθsinθ=41-2cosθsinθ      --[using cos2θ+sin2θ=1]=41-sin2θ                --[using 2cosθsinθ=sin2θ]since value of sinθ can lie between 0 to 1hence Range of sin2θ∈0,1now Range of 1-sin2θ ∈0,1∴ Range of 41-sin2θ ∈0,4
thus option a is correct

Regards

Q. If z=z+iy and x 2 + y 2 = 16, then what is the range of ||x-|-|y||?

Q. If z=z+iy and $x^{2} + y^{2}$ = 16, then what is the range of ||x-|-|y||?