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

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Oct 17, 2017

Answer:

#(sqrt(2)-1)/2-i*(sqrt(3)-sqrt(2))/2#

Explanation:

#e^(pi/4*i)#

=#cos(pi/4)+i*sin(pi/4)#

=#sqrt(2)/2+i*sqrt(2)/2#

#e^(pi/3*i)#

=#cos(pi/3)+i*sin(pi/3)#

=#1/2+i*sqrt(3)/2#

Hence,

#e^(pi/4*i)-e^(pi/3*i)=(sqrt(2)-1)/2+i*(sqrt(2)-sqrt(3))/2#

=#(sqrt(2)-1)/2-i*(sqrt(3)-sqrt(2))/2#

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