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Sketch the subsets of the Argand diagram -

Draw near labelled sketched to indicate each of the subsets of the Argand diagram described below.

  1. $\{z: |z|\ge 1\text{ and }0\le\operatorname{Arg} z\le\frac\pi3\}$
  2. $\{z:z+\bar z\gt 0\} $

I can solve Question 1 , but I am not sure about Question 2. Can someone please help.

[Original scan]

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    $\begingroup$ $z + \bar{z} \gt 0 \iff \frac{z + \bar{z}}{2} \gt 0 \iff Re(z) \gt 0$. So it's the solid region to the right of the imaginary axis. $\endgroup$ – Shine On You Crazy Diamond Nov 17 '13 at 0:50
  • $\begingroup$ Where is the question? $\endgroup$ – user85798 Nov 17 '13 at 0:51
  • $\begingroup$ There's is the full question. $\endgroup$ – MATHSUSER Nov 17 '13 at 0:53
  • $\begingroup$ @EnjoysMath does $Re(z) = 2*Re(z)$? $\endgroup$ – Don Larynx Nov 17 '13 at 1:19
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$z + \bar z$ means you add up a complex number and its conjugate and the result must be higher than $0$.

Thus $(a + bi) + (a - bi) = 2a$. Sketch the graph $2*\hspace{2 pt}Re(z)$.

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  • $\begingroup$ Thank you! Understand now. $\endgroup$ – MATHSUSER Nov 17 '13 at 0:55
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Big hint: $$z+\bar{z}=(a+bi)+(a-bi)=2a$$

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