How do you evaluate #e^( ( pi)/12 i) - e^( ( 13 pi)/8 i)# using trigonometric functions?

1 Answer
P dilip_k
Mar 13, 2016

#=0.58+0.38i#

Explanation:

Euler's identity is a special case of Euler's formula from complex analysis, which states that for any real number x,
#e^{ix} = cos x + isin x#
using this formula we have

#e^{ipi/12} -e^{i13pi/12} #
#= cos (pi/12)+ isin (pi/12)-cos (13pi/8)- isin (13pi/8)#
#= cos (pi/12)+ isin (pi/12)-cos (pi+5pi/8)- isin (pi+5pi/8)#
#= cos (pi/12)+ isin (pi/12)+cos (5pi/8)+isin (5pi/8)#
#=0.96-0.54i-0.38+0.92i=0.58+0.38i#

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