complex no. (1 Viewer)

=)(= · Nov 9, 2022

I am not sure how to do part iii

chilli 412 · Nov 9, 2022

=)(= said:
View attachment 36972
I am not sure how to do part iii

this isnt much help but is this from the further complex numbers topic? and how did you do part ii)

=)(= · Nov 9, 2022

chilli 412 said:
this isnt much help but is this from the further complex numbers topic? and how did you do part ii)

not sure, for ii oa and ab have an angle of 90 between them due to a tangent being perpendicular to the radi of a circle hence it is purely imaginary

Drongoski · Nov 9, 2022

Let OAEB be a //gram.
$\overrightarrow {OE} = z_1 + z_2 \\ \\ \overrightarrow {DB} =\overrightarrow {DO} + \overrightarrow {OB} = z_1 + z_2 \\ \\ \overrightarrow {DB} = \overrightarrow {OE} \implies DOEB \text { is a //gram } \\ \\ \overrightarrow {AB} = z_2 - z_1 \\ \\ \overrightarrow {AC} = z_3 - z_1$

DOEB is a //gram $\implies \angle BDO (\phi) = \angle BEO (\theta)$ (opp angles)

OAEB is a //gram $\implies \angle EOA = \angle BEO = \theta$ (alternate angles)

$\angle BAC = \angle ADC = \phi$ (circle geometry)

$\therefore \theta = \phi$

(Now what am I trying to prove?? Well . . .)

$Arg \left ( \frac {z_3 - z_1}{z_2 - z_1} \right ) = \angle BAC = \phi \\ \\ Arg \left ( \frac {z_1 + z_2}{z_1} \right ) = \angle AOE = \angle BEO = \theta \\ \\ \text {and } \theta = \phi$

A very muddled proof!!

chilli 412 · Nov 9, 2022

Drongoski said:
Let OAEB be a //gram.
$/ang F$

latex champ

=)(= · Nov 9, 2022

Drongoski said:
Let OAEB be a //gram.
$\overrightarrow {OE} = z_1 + z_2 \\ \\ \overrightarrow {DB} =\overrightarrow {DO} + \overrightarrow {OB} = z_1 + z_2$

.: DOEB is a //gram $\implies \angle BDO = \angle BEO$

sorry I still don't quite get it

Drongoski · Nov 9, 2022

chilli 412 said:
latex champ

Thank you. You know I struggle with LaTeX. Now you know why my proof comes out in dribs and drabs.

=)(= · Nov 9, 2022

ahhh i get it know thank you, lmao 'dribs and dabs'

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complex no. (1 Viewer)

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chilli 412

oo la la

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Drongoski

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chilli 412

oo la la

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Drongoski

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