# complex numbers help please

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• Apr 22nd 2013, 10:01 AM
righteous818
complex numbers help please
Draw the points A : i
and the point B: (1/(20.5)) + (1/(20.5))i on a argand digram and hence find the argument of A+B i drew it but i am clueless
• Apr 22nd 2013, 10:30 AM
Plato
Re: complex numbers help please
Quote:

Originally Posted by righteous818
Draw the points A : i
and the point B: (1/(20.5)) + (1/(20.5))i on a argand digram and hence find the argument of A+B i drew it but i am clueless

$\arg (i) = \frac{\pi }{2}\;\& \;\arg \left( {\frac{{\sqrt 2 }}{2} + \frac{{\sqrt 2 }}{2}i} \right) = \frac{\pi }{4}$

The $\arg(A+B)=\arctan\left(\frac{\sqrt2+2}{\sqrt2} \right)$
• Apr 22nd 2013, 10:34 AM
righteous818
Re: complex numbers help please
they the mark scheme has 3pi/8 and specifically gave no marks for using that forumla and approximating the answer to 3pi/8, they said not to use that formula, they stressed to use the argand diagram to find it, any suggestions how, i did this first but then realised that they did not accept this method..please help

i forgot to mention they want the argument exactly in terms of pi, and have no marks for find A+B and finidnging the argument from that
• Apr 22nd 2013, 11:15 AM
emakarov
Re: complex numbers help please
Attachment 28083

Note that OACB is a parallelogram, and thus OC is the bisector of ∠AOB.
• Apr 22nd 2013, 11:33 AM
righteous818
Re: complex numbers help please
what is the program you use to plot the function an show it is a paralleogram
• Apr 22nd 2013, 11:43 AM
emakarov
Re: complex numbers help please
To draw the diagram I used TikZ, and to prove that it is a parallelogram I used my wetware.