Cool complex numbers

Algebra Level 1

If z=3+4i, what is the value of z 3 3 z 2 + 5 z + 7 z^{3}-3z^{2}+5z+7 ?

Details and assumptions: 1 \sqrt{-1} is the imaginary unit.

56 23+6i -74-8i -36-8i

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1 solution

Factorize the first two terms collecting z^2 in order to leave (z-3) which is simply 4i. This will make calculations faster.

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