Mathematics Complex Numbers

Let A(z1), B(z2) and C(z3) be three distinct complex numbers such that |z1| = |z2| = |z3| = |z1 + z2 + z3| = 2 and |z1 - z2| = |z1 - z3|. If D is any point on the arc BC other than A, then the value of ∠ADC is:

1
π/6
2
π/5 
3
π/4 
4
π/3 

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