Sunday, 10 August 2014

How does the complex exponential function transform the unit circle?

I know you can write every complex number on the unit circle as eiθ=cos(θ)+isin(θ). But what does it look like when you raise e to the values? You get ecos(θ)+isin(θ)=ecos(θ)(cos(sin(θ))+isin(sin(θ))), but I'm having trouble visualizing this.

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real analysis - How to find limhrightarrow0fracsin(ha)h

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