If z1z2 - C- z12-z22 - R- z1z12-3z22-2 and z23z12-z22-11- then the value of z12-z22 is

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Complex Numbers

If z1z2 ∈ C...

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If $z_{1} z_{2} \in C, z_{1}^{2} + z_{2}^{2} ϵ R, z_{1} (z_{1}^{2} - 3 z_{2}^{2}) = 2$ and $z_{2} (3 z_{1}^{2} - z_{2}^{2}) = 11$ , then the value of $z_{1}^{2} + z_{2}^{2}$ is

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z_{1} z_{2} \in C, {z_{1}}^{2} + {z_{2}}^{2} \in R, z_{1} ({z_{1}}^{2} - 3 {z_{2}}^{2}) = 2

z_{2} (3 {z_{1}}^{2} - {z_{2}}^{2}) = 11

{z_{1}}^{2} + {z_{2}}^{2}

Z_{1}, Z_{2} \in C

Z_{1}^{2} + Z_{2}^{2} \in R

Z_{1} (Z_{1}^{2} - 3 Z_{2}^{2}) = 10

Z_{2} (3 Z_{1}^{2} - Z_{2}^{2}) = 30

(Z_{1}^{2} + Z_{2}^{2})

z_{1}, z_{2}

(z_{1} \neq z_{2})

| z_{1}^{2} - z_{2}^{2} | = | ¯ ¯¯¯ ¯ z_{1}^{2} + ¯ ¯¯¯ ¯ z_{2}^{2} - 2 {¯ ¯ ¯ z}_{1} {¯ ¯ ¯ z}_{2} |

z_{1}

z_{2}

∣ ∣ z_{1} + \sqrt{{z_{1}}^{2} - {z_{2}}^{2}} ∣ ∣ + ∣ ∣ z_{1} - \sqrt{{z_{1}}^{2} - {z_{2}}^{2}} ∣ ∣

0, z_{1} and z_{2}

z_{1}^{2} + z_{2}^{2} = z_{1} z_{2}

z_{0}

z_{1}^{2} + z_{2}^{2} = 3 z_{0}^{2}

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