Mathegoras

Complex numbers › The complex plane › Extremes of the modulus

Minimum of a hyperbola distance expression

University · ●●●●○ 100 pts

Let complex numbers z1z_1 and z2z_2 satisfy Re⁡z1>0\operatorname{Re} z_1>0, Re⁡z2>0\operatorname{Re} z_2>0, and Re⁡(z12)=Re⁡(z22)=2\operatorname{Re}(z_1^2)=\operatorname{Re}(z_2^2)=2. Find the minimum value of ∣z1+2∣+∣z2‾+2∣−∣z1‾−z2∣|z_1+2|+|\overline{z_2}+2|-|\overline{z_1}-z_2|. Round to two decimal places.

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hyperbolastriangle inequality