How can you use trigonometric functions to simplify # 2 e^( ( pi)/3 i ) # into a non-exponential complex number?

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Answer 1 · 2018-03-25T08:05:58

The answer is #=1+isqrt3#

Apply Euler's Identity

#e^(i theta)=costheta+isintheta#

Here,

#z=2e^(ipi/3)#

#=2(cos(pi/3)+isin(pi/3))#

#cos(pi/3)=1/2#

#sin(pi/3)=sqrt3/2#

Therefore,

#z=2(1/2+isqrt3/2)#

#=1+isqrt3#