Question

The complex number z is given by
z=(√3)+i.

On a sketch of an Argand diagram with origin O, show the points A and B representing the complex numbers z and iz* respectively. Prove that angle AOB=1/6 π .

Answer 1

@Michele_Laino

Answer 2

@zepdrix

Answer 3

@Preetha

Answer 4

what is the modulus of your complex number?

Answer 5

2

Answer 6

ok! now we have to determine the pricipal argument, so we have to compute these quantiities:
\[\Large \begin{gathered}
\cos \theta = \frac{{\Re z}}{{\left| z \right|}} = ...? \hfill \\
\sin \theta = \frac{{\Im z}}{{\left| z \right|}} = ...? \hfill \\
\end{gathered} \]
what is \theta?

Answer 7

there |z|=2

Answer 8

yes

Answer 9

hint:
\[\Large \begin{gathered}
\cos \theta = \frac{{\Re z}}{{\left| z \right|}} = \frac{{\sqrt 3 }}{2} \hfill \\
\sin \theta = \frac{{\Im z}}{{\left| z \right|}} = \frac{1}{2} \hfill \\
\end{gathered} \]
so, what is \theta, please?

Answer 10

wait

Answer 11

1/sqrt 3

Answer 12

no, \theta has to be an angle, like pi/2, pi/8, and so on

Answer 13

wait wait

Answer 14

pi/6

Answer 15

that's right!

Answer 16

what about the argand diagram ?

Answer 17

we have to plot z and iz*

what about the iz*

i know for z only

Answer 18

please wait I redo my drawing

Answer 19

yes