Question #8e2b3

1 Answer
Oct 16, 2017

#-1/i#

Explanation:

  • By the rule #color(red)(a^(-b)=1/(a^b)#

#=i^(-39)=1/(1^39)#

  • By the rule #color(red)(a^(m*n)=(a^m)^n#

#=1/(1^39)=1/(i(i^2)^19#

  • By the rule #color(red)(i^2=-1#

#1/(i(i^2)^19)=1/((-1)^19i)=1/(-1^19i)# [As 19 is odd]

  • As #color(red)(1^19=1#

#1/(-1^19i)=1/-i=-1/i#