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Gosha

Member

From: Russia

Joined: 2015-03-15

Posts: 6,211

Help me with my home work

i have an equation:

i found roots for that equation:
1)
2)
3)

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

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

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

Yu

Guest

Re: Help me with my home work

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

TaskManager

Formerly maxi123

From: i really should update this

Joined: 2015-03-01

Posts: 9,465

Re: Help me with my home work

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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signature by HG, profile picture by bluecloud, thank!!
previous signature by drstereos

Gosha

Member

From: Russia

Joined: 2015-03-15

Posts: 6,211

Re: Help me with my home work

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

LukeM

Member

From: England

Joined: 2016-06-03

Posts: 3,009

Website

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

TaskManager

Formerly maxi123

From: i really should update this

Joined: 2015-03-01

Posts: 9,465

Re: Help me with my home work

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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signature by HG, profile picture by bluecloud, thank!!
previous signature by drstereos

Gosha

Member

From: Russia

Joined: 2015-03-15

Posts: 6,211

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

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

Gosha

Member

From: Russia

Joined: 2015-03-15

Posts: 6,211

Re: Help me with my home work

Here is the result of anyone wonders

Norwee

Formerly NorwegianboyEE

From: Norway

Joined: 2015-03-16

Posts: 3,773

Re: Help me with my home work

The world has been saved!

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