148/VB01. problem / Math - Solved Math Problems

MR-148 / 7. problem

Calculate the value of the following expression:

$f (z) = - z^{3} + 3 z^{2} + z + 2 f (3 + 2 i)$

$f (z) = - z^{3} + 3 z^{2} + z + 2 f (3 + 2 i) = ?$

$f (3 + 2 i)$

$= - {(3 + 2 i)}^{3} + 3 {(3 + 2 i)}^{2} + (3 + 2 i) + 2$

$= - [27 + 3 \cdot 3^{2} \cdot 2 i + 3 \cdot 3 \cdot {(2 i)}^{2} + {(2 i)}^{3}] + 3 \cdot [9 + 2 \cdot 3 \cdot 2 i + {(2 i)}^{2}] + 3 + 2 i + 2$

$= - [27 + 54 i + 9 \cdot 4 i^{2} + 8 i^{3}] + 3 \cdot [9 + 12 i + 4 i^{2}] + 3 + 2 i + 2$

$= - 27 - 54 i - 36 (- 1) - 8 (- i) + 27 + 36 i + 12 (- 1) + 3 + 2 i + 2$

$= + 36 - 12 + 3 + 2 + (- 54 + 8 + 36 + 2) i$

$= 29 - 8 i$

$f (3 + 2 i) = 29 - 8 i$

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