# Complex Numbers - Sketching on Argand Diagram

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.

• $z + \bar{z} \gt 0 \iff \frac{z + \bar{z}}{2} \gt 0 \iff Re(z) \gt 0$. So it's the solid region to the right of the imaginary axis. – StudySmarterNotHarder Nov 17 '13 at 0:50
• Where is the question? – user85798 Nov 17 '13 at 0:51
• There's is the full question. – MATHSUSER Nov 17 '13 at 0:53
• @EnjoysMath does $Re(z) = 2*Re(z)$? – Don Larynx Nov 17 '13 at 1:19

$z + \bar z$ 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 $2*\hspace{2 pt}Re(z)$.
Big hint: $$z+\bar{z}=(a+bi)+(a-bi)=2a$$