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The conjugate of a complex number $z = x + j y$ is given by $z^* = x - j y$. When $z$ is written in polar form as $z = r e^{j \theta}$, the complex conjugate is given by $z^* = r e^{-j \theta}$. In general, to compute the conjugate of a complex number, replace $j$ by $-j$ everywhere.


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