Paired Complex Numbers

★ 6/10complex numbersPolarization Identity

Problem

Complex numbers z1,z2,z3,z4z_1, z_2, z_3, z_4 satisfy

∣z1∣2+∣z2∣2=∣z3∣2+∣z4∣2=4,z1z3‾+z2z4‾=0.|z_1|^2 + |z_2|^2 = |z_3|^2 + |z_4|^2 = 4, \qquad z_1\overline{z_3} + z_2\overline{z_4} = 0.

Find ∣z1z4−z2z3∣\left|z_1 z_4 - z_2 z_3\right|.

Answer

Solution

Difficulty6/10
Topicscomplex numbers, Polarization Identity

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