Complex Equation Solving

Algebra Level 4

If AA and BB are real numbers, and the following is true:

Aeiπ/3+Beiπ/6=2eiπ/4\large{A e^{i \pi/3} + B e^{i \pi/6} = \sqrt{2} e^{-i \pi/4}}

What is AB\large{\frac{A}{B}}?

Note: i=1i = \sqrt{-1}

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