Originally posted by Mexico(i)(i) = 2i
square root of -i hmmmmm.......
square root od (-1 X (root -1) = (root -1) X (root -1)
(root -1)(root -1) = (i)(i) = 2i = Aye Aye Captn' and a lot of rooting?
Nope. the product of the absolute value cannot be established without a positive. ??
take it to debates, Mike, spankey! 😉
Multiplying Positive and Negative Numbers
To multiply a pair of numbers if both numbers have the same sign, their product is the product of their absolute values (their product is positive). If the numbers have opposite signs, their product is the opposite of the product of their absolute values (their product is negative). If one or both of the numbers is 0, the product is 0.
This can't be done with (i) x (i)/.... cannot be positive.....or negative...
Originally posted by mikelomBut it's still 2i, I believe anyway..., Been a long time.... But you have to remember that i is a concept rather than a true number.... Thus the rules can be bent here, thats as far as I remember....
(i)(i) = 2i
Nope. the product of the absolute value cannot be established without a positive. ??
take it to debates, Mike, spankey! 😉
Multiplying Positive and Negative Numbers
To multiply a pair of numbers if both numbers have the same sign, their product is the product of their absolute values (their product is positive). If the numbers have opp ...[text shortened]... he product is 0.
This can't be done with (i) x (i)/.... cannot be positive.....or negative...
Ill take it to posers and puzzles see what they have to say about it.....
Originally posted by MexicoI totally love your "Silence is golden. Duct tape is silver." It's almost worthy of its own thread!
But it's still 2i, I believe anyway..., Been a long time.... But you have to remember that i is a concept rather than a true number.... Thus the rules can be bent here, thats as far as I remember....
Ill take it to posers and puzzles see what they have to say about it.....
Originally posted by mikelomwe seek a complex number a+bi, whose square: (a^2 - b^2) + (2ab)i = -i
(i)(i) = 2i
Nope. the product of the absolute value cannot be established without a positive. ??
take it to debates, Mike, spankey! 😉
Multiplying Positive and Negative Numbers
To multiply a pair of numbers if both numbers have the same sign, their product is the product of their absolute values (their product is positive). If the numbers have opp ...[text shortened]... he product is 0.
This can't be done with (i) x (i)/.... cannot be positive.....or negative...
so we seek a simultaneous solution to
(1) a^2 - b^2 = 0 and
(2) 2ab = -1.
clearly by equation (1), a=b will give us one solution. then by (2), a=b= [sqrt(2)/2]*i, and our complex number a+bi = [sqrt(2)/2]i - [sqrt(2)/2]i^2 or finally
[sqrt(2)/2]i - sqrt(2)/2
the other solution is given by a=-b. so then a = [sqrt(2)/2] and b = -[sqrt(2)/2].
so a + bi = [sqrt(2)/2] - [sqrt(2)/2]i.
Originally posted by MexicoBlown away. 🙂
we seek a complex number a+bi, whose square: (a^2 - b^2) + (2ab)i = -i
so we seek a simultaneous solution to
(1) a^2 - b^2 = 0 and
(2) 2ab = -1.
clearly by equation (1), a=b will give us one solution. then by (2), a=b= [sqrt(2)/2]*i, and our complex number a+bi = [sqrt(2)/2]i - [sqrt(2)/2]i^2 or finally
[sqrt(2)/2]i - sqrt(2)/2
the other solut ...[text shortened]... by a=-b. so then a = [sqrt(2)/2] and b = -[sqrt(2)/2].
so a + bi = [sqrt(2)/2] - [sqrt(2)/2]i.
Originally posted by Grampy BobbyGB, for all the breadth of your education, you appear to have overlooked the obvious resource for information on this matter; the much respected www.bumblebees.org 🙂
According to the age old chestnut, hairy-bodied bumblebees are by aerodynamic definition unable to become airborne,
much less sustain flight. How are mass, weight, gravity and wind current overcome with such a slight wing span?
I am most amused by the concept of a 'tethered bumblebee'
I quote:
'A well-known myth says that scientists once proved that bumblebees should not be able to fly. The myth started from an over-simplified calculation on a napkin at a dinner party. But even detailed models of the flight of the bumblebee are limited because they are based largely on the motion of tethered bumblebees, which behave differently. Now Lijang Zeng of Tsinghua University in China and colleagues have devised a laser system that accurately measures the key parameter in the flight of any insect - its 'body vector' (Lijang Zeng et al 2001 Meas. Sci. Technol. 12 1886).
The apocryphal story about bees not being able to fly arose because the roughness and flexibility of their wings was neglected in a quick calculation. The wings of a bumblebee bend to create vortices that provide lift on both the upward and downward strokes, and a full analysis of the bee's flight involves many factors: wing angle, wing deformation, aerodynamic and inertial forces on the wing, and so on. All of these parameters are expressed in terms of 'body vector' - that is, the exact orientation of the insect's body.
Existing methods for measuring the body vectors of insects in free flight assume that the wings act symmetrically, but this only happens if the insect is flying in a straight line. To measure body vector more accurately, Zeng and colleagues developed technique that accounts for more realistic curved flight paths.
The team glued a sliver of glass weighing just 0.8 milligrams to the top of a bumblebee's body, between its wings. The bumblebee was then allowed to fly freely inside a small clear box, illuminated from above by an array of 49 lasers. As the bumblebee changed direction and orientation, the laser beams bounced off the glass onto a trapezoidal screen suspended above the box.
Synchronized cameras above and at the side of the box monitored the position of the bumblebee and this allowed the team to calculate the angle of reflection of the laser light and then the body vector. Coupled with velocity and acceleration data provided by the cameras, the technique should allow biologists to model insect flight much more precisely. Using the new method, Zeng's team found that the bumblebee's body vector varied considerably, even as it flew in their small experimental chamber.'
I trust this answers your question.
However, I would like to ask why you don't see white dog poo anymore?
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Originally posted by PolicestateAs to education, Mark Twain observed that "We're all ignorant, just on different subjects." Exposed to cyberspace about nine months
GB, for all the breadth of your education, you appear to have overlooked the obvious resource for information on this matter; the much respected www.bumblebees.org 🙂
I am most amused by the concept of a 'tethered bumblebee'
I quote:
'A well-known myth says that scientists once proved that bumblebees should not be able to fly. The myth started fr question.
However, I would like to ask why you don't see white dog poo anymore?
now... roughly equivalent, I would think, to early first grade.
Your dig and find of the comprehensive bumblebee info is fascinating. No idea anyone had ever looked into the question so deeply. Do you
suppose you could attach a shard of beach glass (found along the Swedish Coast) between my shoulders next time I'm at the precinct?
White dog poo question (pleased it's equally arcane) would seem to relate to diet. Near total consumption of commercial chow along with
limited if any raw marrow from real bones would be the only profound change that comes to mind. If true, where are all the bones going?
Great post. Thanks. -gb 🙂
Originally posted by Grampy BobbyLike the Twain quote, hadn't heard it before. I trust you know that my jibe was jovial? If you had heard of bumblebee.org you really would be a man of wide interests, and your education is not in question!
As to education, Mark Twain observed that "We're all ignorant, just on different subjects." Exposed to cyberspace about nine months
now... roughly equivalent, I would think, to early first grade.
Your dig and find of the comprehensive bumblebee info is fascinating. No idea anyone had ever looked into the question so deeply. Do you
suppose you ...[text shortened]... hat comes to mind. If true, where are all the bones going?
Great post. Thanks. -gb 🙂
As for the dog waste, I think your reasoning makes sense, the other theory I have worked out is that in this modern world of litter and dog fouling police, they simply aren't left to age in the sun like they were before. I am sure they turned white after being brown initially.
I have another. Is it really better to have loved and lost, than never to have loved at all? They say grief is the price we pay for love. Although I am fortunate in not having a recent bereavement, it does seem a heavy price to pay?
Open forum....
Originally posted by MexicoMy original post consideres only the non-imaginary.
Yep you can.... Its 5(i)...... Where i is the imaginary number
(squareroot -1)... thus if I have square root of -25 apples then I have 5 apples X (i) the imaginary number..... resulting in 5 imaginary apples..... and a bad acid trip....
This is actually true as well.....
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I see your point; to know what -1 is you have to know what 1 is in the first place however.... Your logic would actually be better suited to 0 because, if we're going to get technical here to know what 1 is you first have to know what 0 is. Otherwise you have no point of reference with which to define 1. To know you have something then you first have to not have it.....
Also in purely mathematical terms 1 is a step away from original point.... Since origin will always be the point (0,0,0).... Or (0,0,0,0,0,0) doesn't actually matter how many dimensions we are dealing with. In 1 dimension origin is still 0. Everything else is simply derived from this.
And 1 = 1+0
And 0 = any number x 0
And X/0 = Apocalypse, thus 0 is all powerful (Although I have heard that chuck norris can divide by 0)