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If I have e^{4pi*i/3} - e^{5pi*i/6}, how would I solve that?  Like how do I subtract?  I'm only used to head to tail addition

 Mar 21, 2023
 #1
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We can simplify this expression using the properties of complex exponential functions:

 

e^(4πi/3) - e^(5πi/6) = cos(4π/3) + i sin(4π/3) - cos(5π/6) - i sin(5π/6)

 

= (-1/2) + (sqrt(3)/2)i - (sqrt(3)/2) - (1/2)i

 

= -1 - (sqrt(3)/2)i

 

Therefore, e^(4πi/3) - e^(5πi/6) simplifies to -1 - (sqrt(3)/2)i.

 Mar 21, 2023
 #2
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When I tried that, I got (1-2sqrt(3))+(sqrt(3)+2)i. How did you simplify futher?
GandalftheGrey  Mar 21, 2023

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