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

G iven 0 < x ⩽ \frac{π}{2}, 0 < y ⩽ \frac{π}{2},

Let z_{1} = \frac{\cos x}{\sin y} + \frac{\cos y}{\sin x} i, and ∣ z_{1} ∣= 2;

If z_{2} = \sqrt{x} + \sqrt{y} i, then what is the

maximum value of ∣ z_{1} - z_{2} ∣ .