- #1
MathAmateur
- 67
- 8
I was playing around with complex numbers in Matlab this evening and noticed this interesting pattern:
Given:
[tex]a = (e^{x})^{i \pi/2}[/tex]
When x is incremented an integer power (0,1,2,3), the a is rotated [tex]{\pi/2}[/tex] radians in the complex plane. It started out at 0 radians with x = 0 and then rotated to [tex]{\pi/2}[/tex] radians with x= 1 (the familiar Euler result) and then then to [tex]{\pi}[/tex], etc, around and around the unit circle.
I found this very interesting and just wanted to share it and ask if there were any comments on why this may be so.
Given:
[tex]a = (e^{x})^{i \pi/2}[/tex]
When x is incremented an integer power (0,1,2,3), the a is rotated [tex]{\pi/2}[/tex] radians in the complex plane. It started out at 0 radians with x = 0 and then rotated to [tex]{\pi/2}[/tex] radians with x= 1 (the familiar Euler result) and then then to [tex]{\pi}[/tex], etc, around and around the unit circle.
I found this very interesting and just wanted to share it and ask if there were any comments on why this may be so.
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