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Show that if z(1)z(2)+z(3)z(4)=0 and z(...

Show that if ` z_(1)z_(2)+z_(3)z_(4)=0 and z_(1)+z_(2)=0` ,then the complex numbers ` z_(1),z_(2),z_(3),z_(4)` are concyclic.

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To show that the complex numbers \( z_1, z_2, z_3, z_4 \) are concyclic given the conditions \( z_1 z_2 + z_3 z_4 = 0 \) and \( z_1 + z_2 = 0 \), we can follow these steps: ### Step 1: Use the condition \( z_1 + z_2 = 0 \) From the condition \( z_1 + z_2 = 0 \), we can express \( z_2 \) in terms of \( z_1 \): \[ z_2 = -z_1 \] ...
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