Complex Numbers - Sketching on Argand Diagram

Question

Sketch the subsets of the Argand diagram -

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

$\{z: |z|\ge 1\text{ and }0\le\operatorname{Arg} z\le\frac\pi3\}$

$\{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]

$z + \bar{z} \gt 0 \iff \frac{z + \bar{z}}{2} \gt 0 \iff Re(z) \gt 0$. So it's the solid region to the right of the imaginary axis. — Daniel Donnelly, Nov 17 '13 at 00:50

score 2 · Accepted Answer · answered Nov 17 '13 at 00:50

2

$z + \bar z$ 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 $2*\hspace{2 pt}Re(z)$.

answered Nov 17 '13 at 00:50

Don Larynx

4,703

Thank you! Understand now. – MATHSUSER Nov 17 '13 at 00:55

score 1 · Answer 2 · answered Nov 17 '13 at 00:52

1

Big hint: $$z+\bar{z}=(a+bi)+(a-bi)=2a$$

answered Nov 17 '13 at 00:52

Dan Rust

30,108

Complex Numbers - Sketching on Argand Diagram

2 Answers2