Menu Close

Given-0-lt-x-pi-2-0-lt-y-pi-2-Let-z-1-cos-x-sin-y-cos-y-sin-x-i-and-z-1-2-If-z-2-x-y-i-then-what-is-the-maximum-value-of-z-1-z-2-




Question Number 107571 by ZiYangLee last updated on 11/Aug/20
Given 0<x≤(π/2), 0<y≤(π/2),  Let z_1 =((cos x)/(sin y))+((cos y)/(sin x)) i ,and ∣z_1 ∣=2 ;  If z_2 =(√x)+(√(y ))i ,then what is the  maximum value of ∣z_1 −z_2 ∣.
$${G}\mathrm{iven}\:\mathrm{0}<\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}},\:\mathrm{0}<\mathrm{y}\leqslant\frac{\pi}{\mathrm{2}}, \\ $$$$\mathrm{Let}\:{z}_{\mathrm{1}} =\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{y}}+\frac{\mathrm{cos}\:{y}}{\mathrm{sin}\:{x}}\:{i}\:,\mathrm{and}\:\mid{z}_{\mathrm{1}} \mid=\mathrm{2}\:; \\ $$$$\mathrm{If}\:{z}_{\mathrm{2}} =\sqrt{{x}}+\sqrt{{y}\:}{i}\:,\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mid{z}_{\mathrm{1}} −{z}_{\mathrm{2}} \mid. \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *