How do you evaluate eπ12ie13π8i 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,
eix=cosx+isinx
using this formula we have

eiπ12ei13π12
=cos(π12)+isin(π12)cos(13π8)isin(13π8)
=cos(π12)+isin(π12)cos(π+5π8)isin(π+5π8)
=cos(π12)+isin(π12)+cos(5π8)+isin(5π8)
=0.960.54i0.38+0.92i=0.58+0.38i