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so, rather than read and absorb information from someone who has a firm grasp on your proposal
the increasing exponent, then, represents a phase change (sign change) as consecutive rotations of the vector. this is similar to the activity you have described.
Geometrically, they are very easy to understand. A complex number
Originally posted by ChaoticOrder
reply to post by Moduli
Geometrically, they are very easy to understand. A complex number
Well done on being the 5 millionth person in this thread to say exactly what you just said.
Wow your intelligence is really awe inspiring... you have convinced me.edit on 15/6/2013 by ChaoticOrder because: (no reason given)
if you cannot understand why segregating the real and imaginary components of a complex number is purposeless, then you have not understood the fundamental reason for having an imaginary unit.
if you wish to combine a real and imaginary number, you must solve for the modulus or take the dot-product. this is because both of these numbers retain a geometric interpretation.
Originally posted by SevenThunders
Why stop at imaginary numbers? Why not look at quaternions, biquaternions and clifford numbers?
They turn out to be very useful in physics and engineering. Rotations in 3 and 4 space and even Lorenz transformations are readily described by quaternions. Imaginary numbers have deep geometric meaning.
Why stop at imaginary numbers? Why not look at quaternions, biquaternions and clifford numbers?
To compensate all the signs are reversed on the directly related operations, we kind of operate in a mirror reflection of the calculation plane so √-1 does exist, but at the cost of making √1 unreachable in this imaginary plane.
What I am proposing is when √-1 pops up, our ruler went into negative numbers when measuring one side of the table.
Mandelbrot Set is connected.