#e^((11pi)/8i)*e^((pi/2)i)#
#e^((11pi)/8i) = cos((11pi)/8) + isin((11pi)/8)#
#e^((pi/2)i) = cos(pi/2) + isin(pi/2)#
#e^((11pi)/8i)*e^((pi/2)i)#
# = (cos((11pi)/8) + isin((11pi)/8))*(cos(pi/2) + isin(pi/2))#
#=cos((11pi)/8+pi/2)+isin((11pi)/8+pi/2)#
#=cos((11pi)/8+(4pi)/8)+isin((11pi)/8+(4pi)/4)#
#=cos((11+4)pi/8) + isin((11+4)pi/8)#
#=cos((15pi)/8)+isin((15pi)/8)#
Note: The question said in trigonometric form so converted to trigonometric form and multiplied. Using Euler's form would be easy multiply and then convert, the choice is yours.
Alternate method:
#e^((11pi)/8i)*e^((pi/2)i)#
#=e^(((11pi)/8+pi/2)i)# using exponent rule #a^m*a^n=a^(m+n)#
#=e^(((15pi)/8)i)#
Use the Euler's formula
#=cos((15pi)/8) + isin((15pi)/8)# Answer.
