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Question: How to simplify this expression?

Question:How to simplify this expression?

Rouben Rostamian 8003 Maple
complex simplify
February 10 2019
1

I don't know how to simplify the expression A/B in the worksheet below.  I know that it should simplify to exp(I*Pi/3).  How do I lead Maple to discover that result without telling it the solution ahead of the time?  All variables other than A and B are real.

> 

restart;
> 

local gamma:
> 

A := I*sqrt(3) + 2*c*exp(I*(gamma+(1/3)*Pi)) + 2*a*exp(I*alpha) - 2*a*exp(I*(alpha+(1/3)*Pi)) - 2*b*exp(I*beta) - 1;

I*3^(1/2)+2*c*exp(I*(gamma+(1/3)*Pi))+2*a*exp(I*alpha)-2*a*exp(I*(alpha+(1/3)*Pi))-2*b*exp(I*beta)-1

> 

B := I*sqrt(3) - 2*a*exp(I*(alpha+(1/3)*Pi)) - 2*b*exp(I*beta) + 2*b*exp(I*(beta+(1/3)*Pi)) + 2*c*exp(I*gamma) + 1;

I*3^(1/2)-2*a*exp(I*(alpha+(1/3)*Pi))-2*b*exp(I*beta)+2*b*exp(I*(beta+(1/3)*Pi))+2*c*exp(I*gamma)+1

How to show that A/B = e^((1/3)*i*Pi)?

 

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