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Kitten

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I am trying to calculate a pole of f(z)=http://www4b.wolframalpha.com/Calculate/MSP/MSP86721gicihdh283d613000033ch4ae4eh37cbd4?MSPStoreType=image/gif&s=35&w=44.&h=40. . The answer in the textbook is:

Simple pole at http://www4f.wolframalpha.com/Calculate/MSP/MSP2485217c56eb3b13h612000056di60dga07378cd?MSPStoreType=image/gif&s=14&w=52.&h=26. and a simple pole at http://www4f.wolframalpha.com/Calculate/MSP/MSP2292204iia97b59e96db00001591c4be13e5ge82?MSPStoreType=image/gif&s=19&w=66.&h=24.

Trying to get to the same solution:

So far I have that z=±√ i

I need to find this pole in terms of z=re^iθ so I’m trying to plot this on an argand diagram but I don’t know how.

Since z=x+iy, I assumed that the real part is 0 and the imaginary part is ±1 but plotting this gives me

θ/2 and not over 4 which is required.

Simple pole at http://www4f.wolframalpha.com/Calculate/MSP/MSP2485217c56eb3b13h612000056di60dga07378cd?MSPStoreType=image/gif&s=14&w=52.&h=26. and a simple pole at http://www4f.wolframalpha.com/Calculate/MSP/MSP2292204iia97b59e96db00001591c4be13e5ge82?MSPStoreType=image/gif&s=19&w=66.&h=24.

Trying to get to the same solution:

So far I have that z=±√ i

I need to find this pole in terms of z=re^iθ so I’m trying to plot this on an argand diagram but I don’t know how.

Since z=x+iy, I assumed that the real part is 0 and the imaginary part is ±1 but plotting this gives me

θ/2 and not over 4 which is required.

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