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Complex numbers › Complex arithmetic › Conjugates

Minimise |z|² under a conjugate constraint

University · ●●○○○ 20 pts

Over complex numbers zz, minimize z∗zz^*z subject to z=z∗+iz = z^* + i, where z∗z^* is the complex conjugate of zz. Write the minimizing zz as z=a+biz = a + bi with real aa and bb, and find aa and bb.

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Lagrange multipliersconstrained optimizationcomplex conjugate