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1. Minimise |z|² under a conjugate constraint ●●○○○ 20 ptsOver complex numbers $z$, minimize $z^*z$ subject to $z = z^* + i$, where $z^*$ is the complex conjugate of $z$. Write the minimizing $z$ as $z = a + bi$ with real $a$ and $b$, and find $a$ and $b$.