- #1
hoodwink
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When looking at
w^z = e^(z log w)
I understand that adding any integer multiple of (2*pi*i) to log w is equivalent to a full rotation in the complex plane. I don't understand how this step is equivalent to multiplying w^z by e^(z*2*pi*i). Also, I'm missing the significance of this being represented in the complex plane as the intersections of 2 logarithmic spirals. I can see how the first spiral is given by w^z, but the other?
If anyone has a copy handy, my questions arose from looking at pages 96-97 of The Road to Reality by Roger Penrose.
w^z = e^(z log w)
I understand that adding any integer multiple of (2*pi*i) to log w is equivalent to a full rotation in the complex plane. I don't understand how this step is equivalent to multiplying w^z by e^(z*2*pi*i). Also, I'm missing the significance of this being represented in the complex plane as the intersections of 2 logarithmic spirals. I can see how the first spiral is given by w^z, but the other?
If anyone has a copy handy, my questions arose from looking at pages 96-97 of The Road to Reality by Roger Penrose.