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The equations given are:

\[
f_1 = \alpha \left( \frac{(i_0 - i_1)^2}{(c_0 - z_1)^2} - \frac{(i_0 + i_1)^2}{(c_0 + z_1)^2} \right)
\]

\[
f_2 = -\alpha \left( \frac{(i_0 - i_2)^2}{(c_0 - z_2)^2} + \frac{(i_0 + i_2)^2}{(c_0 + z_2)^2} \right)
\]

In order to determine \( i_1 \) and \( i_2 \), we need additional information or conditions such as the values of \( f_1 \) and \( f_2 \), or any constraints on these variables. Could you provide the missing data, or should we explore a specific method to solve for \( i_1 \) and \( i_2 \)?

Would you like to see a step-by-step approach on how we could solve these types of equations? 

### Related Questions:
1. What are the values of \( f_1 \) and \( f_2 \), or are they functions?
2. Are there specific conditions or relationships between \( i_0, z_1, z_2, c_0 \)?
3. Could the equations involve symmetries or simplifications that might aid in solving for \( i_1 \) and \( i_2 \)?
4. Would you like to analyze how these functions behave when \( i_1 \) and \( i_2 \) approach certain limits (e.g., 0 or infinity)?
5. Should we explore numerical methods to solve the system if analytical solutions are complex?

### Tip:
When solving complex equations involving parameters like \( i_1 \) and \( i_2 \), consider simplifying the system by using approximations or analyzing symmetrical behaviors if applicable.

This problem involves solving for i1 and i2 using nonlinear equations that involve quadratic terms, typically encountered in university-level algebra and optimization problems. Step-by-step solutions are explored for these equations.

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