I saw an MCQ in a book that asks that sum of a complex number $Z$ with its Conjugate equals to zero if and only if Im$(Z)=0$. But my brain cannot absorb this answer. Because their sum equals to 2Re$(Z)$, therefore Re$(Z)$ must be zero. Isn't it?
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5The book is wrong. – Jyrki Lahtonen Jul 04 '18 at 08:14
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Seems to me the same thing as you said. – Raju Jul 04 '18 at 08:15
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Can you please recommend me an Objective MCQs book for an undergrad level? I observed a lot of errors and misconceptions in the book I'm studying so I want to leave that book. – Raju Jul 04 '18 at 08:22
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Try Complex Analysis by Theodore W. Gamelin, or the book by Bak and Newman. – Daniel Buck Jul 04 '18 at 09:02
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Considering: $a=Re \ z$ and $b=Im \ z$ $$z+z^*=(a+i \ b)+(a-i \ b)=2a$$
$$2 \ a=0$$ $$a=0$$
Francesco Serie
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I think there; in place of sum it must be difference:
Let $x=Re \ z$ and $y=Im \ z$ $$z-z^*=(x+i \ y)-(x-i \ y)=2i\ y =0$$
$$2 \ y=0$$ $$y=0$$
Sonu Lamba
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