How do you evaluate # e^( ( pi)/4 i) - e^( ( 4 pi)/3 i)# using trigonometric functions?

1 Answer
Nov 14, 2016

# sin ( pi)/4 + i cos ( pi)/4 #
- # sin ( 4 pi)/3 + i cos ( 4 pi)/3 #

Explanation:

In complex terms, #R ( sintheta + i costheta ) #= # Re ^ (i theta) #
where #R# is the modulus and #theta# is the argument.

So
# e^( ( pi)/4 i) - e^( ( 4 pi)/3 i)# = #1 ( sin ( pi)/4 + i cos ( pi)/4 ) #
- #1 ( sin ( 4 pi)/3 + i cos ( 4 pi)/3 ) #

= # sin ( pi)/4 + i cos ( pi)/4 #
- # sin ( 4 pi)/3 + i cos ( 4 pi)/3 #