Complex Plugging

Algebra Level 3

Suppose f(x)=x48x3+4x2+4x+39f(x)=x^4-8x^3+4x^2+4x+39 and f(3+2i)=a+bi f(3+2i)=a+bi.

Find the value of 32ab-32\dfrac{a}{b}.

Details and Assumptions

Here ii is the imaginary unit, which satisfies i2=1i^2=-1.

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