Comments on: Complex Numbers for Rotating, Translating, and Scaling the Plane

By: Peter L.Griffiths

Peter L.Griffiths — Sat, 20 Aug 2011 17:55:58 +0000

Further to my comment of 21 May 2011, the complex number a+ib can be converted into an imaginary number by making a equal 0, and then substituting the Cotes format cos90+isin90 equalling 0+i. It will be recognised that cos180+isin180 equals -1, and cos360+isin360 equals i to the power of 4 which is +1. The same principle also applies for division
cos45+isin45 equals the square root of i. In this way the roots and powers of i, -i, +1 and -1 can be calculated all based on the Cotes format.

By: Peter L. Griffiths

Peter L. Griffiths — Sat, 21 May 2011 16:28:26 +0000

To obtain the roots of the complex number a+ib you take the arcotangent below 90 degrees of the complex ratio a/b and then divide by the root required. The cotangent of the result will give one of the roots of the complex ratio. For the other roots you add 360 degrees and then 720 degrees on to the arcotangent. In this way all n nth integer roots of complex numbers can be obtained.

By: Clifford Algebras for Rotating, Scaling, and Translating Space :: nklein software

Mon, 06 Jul 2009 19:52:06 +0000

[...] using complex numbers for rotating, translating, and scaling the plane [...]

By: Clifford Algebras for Rotating, Scaling, and Translating the Plane :: nklein software

Thu, 11 Jun 2009 18:15:36 +0000

[...] numbers can be used to represent coordinates in the plane and how, once you’ve done that, complex arithmetic leads naturally to rotations, scalings, and translations of the plane. Today, we’re going to do the same with the Clifford algebra [...]

By: pat

pat — Sun, 07 Jun 2009 15:45:38 +0000

I haven’t seen that site. I will check it out.

Thanks…

By: rory

rory — Sun, 07 Jun 2009 13:04:03 +0000

This was a fun read– have you checked out the website khanacademy.org? The guy on there is amazing at explaining basic math stuff.