If `z_1, z_2 in C ,z_1^2+z_2^2 in R ,z_1(z_1^2-3z_2^2)=2 and z_2(3z1^2-z2^2)=11` , then the value of `z1 2+z2 2` is `10` b. `12` c. `5` d. `8`

Explanation

To solve the problem, we need to find the value of \( z_1^2 + z_2^2 \) given the conditions:

1. \( z_1^2 + z_2^2 \in \mathbb{R} \)
2. \( z_1(z_1^2 - 3z_2^2) = 2 \) (Equation 1)
3. \( z_2(3z_1^2 - z_2^2) = 11 \) (Equation 2)

Let's denote \( z_1^2 = x \) and \( z_2^2 = y \).

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