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How do you simplify #1/2(cos(pi/3)+isin(pi/3))div 3(cos(pi/6)+ising(pi/6))# and express the result in rectangular form?

1 Answer

Feb 16, 2017

#1/6 i#

Explanation:

Using Euler's formula,

# cos theta +i sin theta = e^(i theta)#, the given problem reduces to,
#(1/2 e^(i pi/3)) / (3 e^(i pi/6)#

#1/6 e^i( pi/3 -pi/6)#

#1/6 e^(i pi/2)#

#1/6 (cos (pi/2) +i sin (pi/2))#

#1/6 i#....................... [ #cos (pi/2) =0 and sin (pi/2) =1#]

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