arg0 is not undefined , is it? (1 Viewer)

[Mathematician]

the note on the bottom of page 66 in cambridge , says:
"A is excluded from the locus in each case , since z# 1+2i as arg0 is undefined"

z=0 + 0i argz= arctan(0/0) = pi/2 isnt it?

or when they say undefined are they meaning [Like for figure 2.48 b) ] , arg0 # pi/6 ( that is when z= 1+2i)

That better make sense lol.

while im posting this , ill ask a question too.

1,w, w^2 are cube roots of unity.
Show that if the equation z^3-1=0 and pz^5 + qz + r =0 have a common root, then (p+q+r)(pw^5+qw+r)(pw^10+qw^2+r)=0

Is this like that other question i had under "plz solve this annoying problem" ?

 

[spice girl]

Considering complex numbers as vectors, with length and direction.

The argument describes the direction. It is defined as the angle made anticlockwise to the positive real axis.

As you can see, 0 is the zero vector (a special case) length zero, and undefined direction. Thus it has undefined argument.

Anyway, if one of the cube roots of unity was also a root of P(z), then either one of P(1), P(w), P(w^2) would equal zero

Thus (p+q+r)(pw^5+qw+r)(pw^10+qw^2+r)=P(1)P(w)P(w^2) = 0

 

[wogboy]

arctan(0/0) = pi/2 isnt it?

Not true since 0/0 is INDETERMINATE (not necessarily infinite), which means it could actually be any value at all, like 1,100, 20, 78, 10000000000 etc, hence arctan(0/0) does not make sense either (it could be any value at all). You could say that arctan(infinity) = pi/2 and arctan(-infinity) = -pi/2, but 0/0 is not by any means infinity.

+1/0 is infinity and so is +2/0 (in fact any k/0, where k is positive and non zero), so you could find the arctan of these to be pi/2, but not the arctan of 0/0. Likewise you can say that -1/0, -2/0 (or any k/0, where k is neagtive) is equal to -infinity, and the arctan of these to be -pi/2.

Conclusion: Arg(0) *is* undefined, and also indeterminate too.

 

[Mathematician]

...

k thanx all . Thats pretty interesting too(ill remember that).
Im talking about the argument thing.


hahahahahahahahahahhaa, that questions too easy.
I apologise for asking that question.

 

[Harimau]

Question, whats (arctan) ? Is it inverse tan or...? The notation is just different...

 

[ND]

Originally posted by Harimau
Question, whats (arctan) ? Is it inverse tan or...? The notation is just different...

Yep, arctan is inverse tan.

 

[McLake]

Originally posted by Harimau
Question, whats (arctan) ? Is it inverse tan or...? The notation is just different...

arc tan is tan^-1x NOT 1/tanx

 

[wogboy]

Yep, arctan is the inverse of tan, not the reciprical of tan.

that is, if y = tan (x)

then x = arctan(y)

There's a huge difference between the inverse of a function and the reciprical of a function. Don't ever get them confused.

 

[Harimau]

One more question... i heard that tan-1x only gives one value for each of the x value, while arctan gives multiple values as the range of the inverse tan graphs isnt restricted between -90 and 90 degrees.

P.S how do you get the Greater or Equal to sign on VB? and also the inverse tan...