The triangle formed by `A(z_(1)), B(z_(2)) and C(z_(3))` has its circumcentre at origin .If the perpendicular form A to BC intersect the circumference at `z_(4)` then the value of `z_(1)z_(4) + z_(2)z_(3)` is

Explanation

To solve the problem, we need to find the value of \( z_1 z_4 + z_2 z_3 \) given that the circumcenter of triangle \( A(z_1), B(z_2), C(z_3) \) is at the origin and that the perpendicular from \( A \) to line \( BC \) intersects the circumcircle at \( z_4 \).

### Step-by-Step Solution:

1. **Understanding the Geometry**:
The circumcenter of triangle \( ABC \) being at the origin means that the circumcircle of triangle \( ABC \) is centered at the origin in the complex plane. The points \( z_1, z_2, z_3 \) represent the vertices of the triangle.

**Hint**: Remember that the circumcenter is the point equidistant from all vertices of the triangle.
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