Question

Can someone please help me solve this problem!!

Find | z| and Arg( z) for

z=3/(4+2i)
|z|=
Arg(z)=
(Recall −pi< Arg( z)<=pi )

Answer 1

Let me try to help you with this
Remember that the argument of z is given by:

\[\left| z \right| = \sqrt{x^2+y^2}\]
so that in your case
\[\left| z \right| = \sqrt{(3/4)^2+2^2}=\]\[\sqrt{73/16}=(1/4)\sqrt{73}\]

Answer 2

Excuse me, I misread your problem, I didn't see that the complex number is in the denominator. We first need to simply it by complex conjugation.

Answer 3

haha I was just going to ask you about the complex number

Answer 4

but how do we simplify it by complex conjugation

Answer 5

Sorry, let me give it another try, I still have trouble reading these scripts here without the accurate nominator/denominator typeset (-:

Answer 6

ok thanks soo much

Answer 7

Okay here we go again
\[z= (3(4-2i))/((4+2i)(4-2i)) = (12-6i)/(20)=(3/5)-(3/10)i\]
using complex conjugation

Answer 8

what is used to define i?

Answer 9

So this is a form we can work with, unlike the one which is in the problem.
\[\left| z \right|= \sqrt{(3/5)^2+(-3/10)^2}=3/(2\sqrt{5})\]

i is defined as \[i= \sqrt{-1}\] the complex number

Answer 10

So now about the argument, we know by observing the complex conjugated equation that the argument of the Polar coordinates has to be in the IV Quadrant of the Gauss-complex-plane.

So \[\arg=\tan \theta=y/x=(-3/10)/(3/5)=-0.5\]
taking the arctangens of this leads to
\[\theta=-26.5650°\]
which is the argument of the complex number

Answer 11

I hope that helps

Answer 12

Thank you! but it's incorrect!

Answer 13

http://www.wolframalpha.com/input/?i=3%2F%284%2B2i%29 is it? take a look at this.

Answer 14

yea but i dont think that answers the question

Answer 15

Well in this case I misunderstand the problem, from what I remember about complex numbers is that the argument (arg) of a complex number is the angle between the positive x-axis and the complex number. In our case clearly negative.

The \[\left| z \right| \] of a complex number is how far you have to travel from the Origin (0/0) to meet that complex number. Polar coordinates. Maybe you have to wait for other answers to see what they will tell you. However, my computer systems give me identical answers to this problem

Answer 16

ok thanks so much!! i really appreciate your help!

Answer 17

No problem, here again is what my computer calculator gives me as an output to this problem:

radius \[r \approx 0.670820393\]
exact \[r= 3/(2\sqrt{5})\]
\[\theta \approx -26.5651\]

which is consistent with my result. Wait for other replies, take care (-:

Answer 18

Thanks! you too!