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How can you use trigonometric functions to simplify # 12 e^( ( pi)/3 i ) # into a non-exponential complex number?

1 Answer

Shwetank Mauria

Jun 29, 2016

#12e^(pi/3i)=6+6sqrt3i#

Explanation:

A complex number in polar form can be written in two ways -

(a) #re^(itheta)# or (b) #rcostheta+irsintheta#

Hence #12e^(pi/3i)=12cos(pi/3)+i12sin(pi/3)#

= #12xx1/2+ixx12xxsqrt3/2#

= #6+6sqrt3i#

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