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

1 Answer
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