complex exponential

Sirs,
I am going through comllex description I wiki ...
In one place, it is written "eix traces unit circle ... as x ranges through
different real x"
But when I take different values of x such as 30, 45, 60 I see the value of
sinx on x and cosx on y axis eventually leads to values < 1. Only for x eq
0 and 90, I see val eq 1.

Can someone clarify pls that eix does not trace unit circle for all values
of x

Thanks, manish

"manishp" <58525@dsprelated> writes:

> Sirs,
> I am going through comllex description I wiki ...
> In one place, it is written "eix traces unit circle ... as x ranges through
> different real x"
> But when I take different values of x such as 30, 45, 60 I see the value of
> sinx on x and cosx on y axis eventually leads to values < 1. Only for x eq
> 0 and 90, I see val eq 1.
>
> Can someone clarify pls that eix does not trace unit circle for all values
> of x

Manish,

The magnitude r of a point (x, y) in a Cartesian coordinate plane is
defined as 

  r = sqrt(x^2 + y^2).

If 

  x = cos(theta)
  y = sin(theta)

then 

  r = sqrt(cos^2(theta) + sin^2(theta)).

Now there is a trig identity that states 

  cos^2(theta) + sin^2(theta) = 1 

for any value of theta. Thus the radius r of the circle traced by

  x = cos(theta)
  y = sin(theta)

is indeed (precisely) 1, even though the x or y values are less than 1
at certain values of theta.

Basic trigonometry (I learned it in high school). If you don't know it,
learn it ASAP as it is required for this field.
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

On Fri, 14 Jun 2013 22:50:46 -0500, manishp wrote:

> Sirs,
> I am going through comllex description I wiki ... In one place, it is
> written "eix traces unit circle ... as x ranges through different real
> x"
> But when I take different values of x such as 30, 45, 60 I see the value
> of sinx on x and cosx on y axis eventually leads to values < 1. Only for
> x eq 0 and 90, I see val eq 1.
> 
> Can someone clarify pls that eix does not trace unit circle for all
> values of x
> 
> Thanks, manish

I'm not sure what part you're not understanding.  If you plot sin x on 
the x axis, and cos x on the y axis, you should plot a circle with radius 
1.

You're trying to do math experimentally again.  Try looking up your trig 
identities for the value of (cos x)^2 + (sin x)^2.  What is it equal to 
for x a real number?  What does that tell you about e^(i x) and the unit 
circle?

-- 
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

>On Fri, 14 Jun 2013 22:50:46 -0500, manishp wrote:
>
>> Sirs,
>> I am going through comllex description I wiki ... In one place, it is
>> written "eix traces unit circle ... as x ranges through different real
>> x"
>> But when I take different values of x such as 30, 45, 60 I see the
value
>> of sinx on x and cosx on y axis eventually leads to values < 1. Only
for
>> x eq 0 and 90, I see val eq 1.
>> 
>> Can someone clarify pls that eix does not trace unit circle for all
>> values of x
>> 
>> Thanks, manish
>
>I'm not sure what part you're not understanding.  If you plot sin x on 
>the x axis, and cos x on the y axis, you should plot a circle with radius

>1.
>
>You're trying to do math experimentally again.  Try looking up your trig 
>identities for the value of (cos x)^2 + (sin x)^2.  What is it equal to 
>for x a real number?  What does that tell you about e^(i x) and the unit 
>circle?
>
>-- 
>My liberal friends think I'm a conservative kook.
>My conservative friends think I'm a liberal kook.
>Why am I not happy that they have found common ground?
>
>Tim Wescott, Communications, Control, Circuits & Software
>http://www.wescottdesign.com

Thanks. Yes, I should have tried solving on a piece of paper first ...
>

On Fri, 14 Jun 2013 22:50:46 -0500, "manishp" <58525@dsprelated>
wrote:

>Sirs,
>I am going through comllex description I wiki ...
>In one place, it is written "eix traces unit circle ... as x ranges through
>different real x"
>But when I take different values of x such as 30, 45, 60 I see the value of
>sinx on x and cosx on y axis eventually leads to values < 1. Only for x eq
>0 and 90, I see val eq 1.
>
>Can someone clarify pls that eix does not trace unit circle for all values
>of x
>
>Thanks, manish

Hello manish,
  Check the following web page.  It might be of 
some help to you.

http://www.dsprelated.com/showarticle/192.php

[-Rick-]
No. 6: "Where am I?"
No. 2: "In the Village."
No. 6: "What do you want?"
No. 2: "Information."
No. 6: "Who are you?"
No. 2: "I am the new No. 2."
No. 6: "Who is No. 1?"
No. 2: "You are No. 6."
No. 6: "I am not a number. I am a free man!"

>On Fri, 14 Jun 2013 22:50:46 -0500, "manishp" <58525@dsprelated>
>wrote:
>
>>Sirs,
>>I am going through comllex description I wiki ...
>>In one place, it is written "eix traces unit circle ... as x ranges
through
>>different real x"
>>But when I take different values of x such as 30, 45, 60 I see the value
of
>>sinx on x and cosx on y axis eventually leads to values < 1. Only for x
eq
>>0 and 90, I see val eq 1.
>>
>>Can someone clarify pls that eix does not trace unit circle for all
values
>>of x
>>
>>Thanks, manish
>
>Hello manish,
>  Check the following web page.  It might be of 
>some help to you.
>
>http://www.dsprelated.com/showarticle/192.php
>
>[-Rick-]
>No. 6: "Where am I?"
>No. 2: "In the Village."
>No. 6: "What do you want?"
>No. 2: "Information."
>No. 6: "Who are you?"
>No. 2: "I am the new No. 2."
>No. 6: "Who is No. 1?"
>No. 2: "You are No. 6."
>No. 6: "I am not a number. I am a free man!"

Thank you, sir

On 6/14/13 8:50 PM, manishp wrote:
>
> I am going through comlpex description I wiki ...
> In one place, it is written "eix traces unit circle ... as x ranges through
> different real x"
> But when I take different values of x such as 30, 45, 60

um, don't feed degrees into exp(i*theta).  theta should be in radians.



-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."


(coming to you from the Starbucks on the PCH in Malibu.)

On 2013-06-16 00:40, Rick Lyons wrote:
[...]
> No. 6: "Where am I?"
> No. 2: "In the Village."
> No. 6: "What do you want?"
> No. 2: "Information."
> No. 6: "Who are you?"
> No. 2: "I am the new No. 2."
> No. 6: "Who is No. 1?"
> No. 2: "You are No. 6."
> No. 6: "I am not a number. I am a free man!"

Hi Rick,

this signature is new, how it comes?
Big fan of "The Prisoner"?

bye,

-- 

piergiorgio

robert bristow-johnson <rbj@audioimagination.com> writes:
> [...]
> um, don't feed degrees into exp(i*theta).  

Correct. You could kill the poor thing.
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

On Monday, June 17, 2013 5:08:36 AM UTC-5, Randy Yates wrote:
  > robert bristow-johnson <rbj@audio.....com> writes:
  > 
  > 
  > > um, don't feed degrees into exp(i*theta).  
  > 
  > 
  > 
 > Correct. You could kill the poor thing.
 > 
 > -- 
 > 
 > Randy Yates
 > 
 > Digital Signal Labs
 > 
 > http://www.digitalsignallabs.com


Cruel and unusual punishment indeed, since you
are killing the thing by degrees instead of a
swift sharp stroke!