Recall that the conjugate of the complex number ( z=a+b i ) is defined to be ( bar{z}=a-b i ). Prove the following properties of the conjugate: a. ( overline{z+w}= bar{z}+ bar{w} ) b. ( overline{z w}= bar{z} bar{w} ) c. ( bar{z}=z Leftrightarrow z in mathbb{R} ) and ( bar{z}=-z Leftrightarrow i z in mathbb{R} ).

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Recall that the conjugate of the complex number  ( z=a+b i  ) is defined to be  (  bar{z}=a-b i  ). Prove the following properties of the conjugate: a.  (  overline{z+w}= bar{z}+ bar{w}  ) b.  (  overline{z w}= bar{z}  bar{w}  ) c.  (  bar{z}=z  Leftrightarrow z  in  mathbb{R}  ) and  (  bar{z}=-z  Leftrightarrow i z  in  mathbb{R}  ).

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(Solved): Recall that the conjugate of the complex number \( z=a+b i \) is defined to be \( \bar{z}=a-b i \). ...

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