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Differentiation to Solve Modified Sum of Binomial Coefficients

10. If z=3-4i...

Question

10. If z=3-4i then z-3z-3z+99z-95= option A)5 B)6 C)-5 D)-4

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Solution

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z = 3 - 4 i

z^{4} - 3 z^{3} + 3 z^{2} + 99 z - 95

z = e^{2 π i / 3}

1 + z + 3 z^{2} + 2 z^{3} + 2 z^{4} + 3 z^{5}

z

arg (\frac{3 z - 6 - 3 i}{2 z - 8 - 6 i}) = \frac{π}{4}

| z - 3 + 4 i | = 3.

z \in C

| z | < 1

ω = \frac{5 + 3 z}{5 (1 - z)}

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