Let \( A, B \) and \( C \) represent the complex numbers \( \mathrm{z}_{1}, \mathrm{z}_{2}, \mat...

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Let \( A, B \) and \( C \) represent the complex numbers \( \mathrm{z}_{1}, \mathrm{z}_{2}, \mathrm{z}_{3} \) respectively on the complex plane. If the circumcentre of the triangle \( A B C \) lies at the origin, then the orthocentre of triangle \( A B C \) is \( a \mathrm{z}_{1}+b \mathrm{z}_{2}+c \mathrm{z}_{3} \). find \( a+b+c \)
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