Let `z_1, z_2, z_3` be three complex numbers and `a ,b ,c` be real numbers not all zero, such that `a+b+c=0a n da z_1+b z_2+c z_3=0.` Show that `z_1, z_2,z_3` are collinear.

Explanation

To show that the complex numbers \( z_1, z_2, z_3 \) are collinear given the conditions \( a + b + c = 0 \) and \( az_1 + bz_2 + cz_3 = 0 \), we can follow these steps:

### Step 1: Write down the given equations
We have the following two equations:
1. \( a + b + c = 0 \) (Equation 1)
2. \( az_1 + bz_2 + cz_3 = 0 \) (Equation 2)

### Step 2: Express \( c \) in terms of \( a \) and \( b \)
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