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#1 2019-10-17 17:08:58

Gosha
Member
From: Russia
Joined: 2015-03-15
Posts: 6,202

Help me with my home work

i have an equation:
LGMFpA5.png

i found roots for that equation:
1) WaPJHzR.png
2) 7M4q4LC.png
3) 5IZv98x.png

the problem is, i need to visualize these roots on the complex plane, but i have no idea how to do it when they are in trigonometric form, and afaik there is no way to convert it to algebraic form

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#2 2019-10-17 17:29:20

peace
Member
From: admin land
Joined: 2015-08-10
Posts: 9,226

Re: Help me with my home work

there is some sort of smartt maths thingy called if im right wolfram aplha (google it) whihc ca maby help


peace.png

thanks hg for making this much better and ty for my avatar aswell

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#3 2019-10-17 19:05:14

Yu
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Re: Help me with my home work

Great, one more thing that 99% of the world will forget the second they graduate.

#4 2019-10-17 19:45:09

TaskManager
Formerly maxi123
From: i really should update this
Joined: 2015-03-01
Posts: 9,457

Re: Help me with my home work

Yu wrote:

Great, one more thing that 99% of the world will forget the second they graduate.

Excuse me, but complex analysis is actually a field of mathematics that finds application in real life, for example, it is used in electromagnetism branch of physics.
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#5 2019-10-17 20:14:54, last edited by Gosha (2019-10-17 20:15:07)

Gosha
Member
From: Russia
Joined: 2015-03-15
Posts: 6,202

Re: Help me with my home work

Yu wrote:

Great, one more thing that 99% of the world will forget the second they graduate.

if i weren't interested in this i would've gone to this field to study complex numbers

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#6 2019-10-17 21:44:43, last edited by LukeM (2019-10-17 21:46:55)

LukeM
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From: England
Joined: 2016-06-03
Posts: 3,009
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Re: Help me with my home work

This form is useful because cos θ + i sin θ represents a unit vector from the origin at angle θ anti-clockwise from the positive real axis, so that form effectively says that the lines from the origin to those points are of length root6(12) at angles -π/9, 5π/9, and 11π/9. When you plot these you'll also notice something else but I won't spoil the surprise just in case you haven't seen it yet //forums.everybodyedits.com/img/smilies/smile

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#7 2019-10-17 21:54:36

TaskManager
Formerly maxi123
From: i really should update this
Joined: 2015-03-01
Posts: 9,457

Re: Help me with my home work

LukeM wrote:

at angles -π/9, 5π/9, and 11π/9. When you plot these you'll also notice something else but I won't spoil the surprise just in case you haven't seen it yet

i instantly suspected something because i noticed that 5п/9 - (-п/9) = 11п/9 - 5п/9
but yeah i plotted it and that looks pretty cool


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#8 2019-10-18 06:46:24

Gosha
Member
From: Russia
Joined: 2015-03-15
Posts: 6,202

Re: Help me with my home work

LukeM wrote:

This form is useful because cos θ + i sin θ represents a unit vector from the origin at angle θ anti-clockwise from the positive real axis, so that form effectively says that the lines from the origin to those points are of length root6(12) at angles -π/9, 5π/9, and 11π/9. When you plot these you'll also notice something else but I won't spoil the surprise just in case you haven't seen it yet //forums.everybodyedits.com/img/smilies/smile

Thanks, I also posted it on Reddit and got an answer
I knew about the symmetry, I knew about length or the vector and it's angles. But I only did that 1-2 times in class, so when I got home I got lost with cos() and sin()
Should've remembered that angle is the actual angle of the vector, no need for any cos sin calculations

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#9 2019-10-18 06:48:25

Gosha
Member
From: Russia
Joined: 2015-03-15
Posts: 6,202

Re: Help me with my home work

Here is the result of anyone wonders
S2GhaFI.jpg

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#10 2019-10-18 08:32:10

Norwee
Formerly NorwegianboyEE
From: Norway
Joined: 2015-03-16
Posts: 3,772

Re: Help me with my home work

The world has been saved!


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