Evaluate and write in standard form: ${(- 3 + 2 i)}^{2} - 3 (3 - i) (- 2 + 2 i)$ , where $i^{2} = - 1$

17 + 36 i

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17 - 36 i

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- 17 - 36 i

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- 17 + 36 i

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Solution

The correct option is B $17 - 36 i$
Consider $(- 3 + 2 i)^{2} - 3 (3 - i) (- 2 + 2 i)$
$\Rightarrow (- 3 + 2 i)^{2} - 3 (3 - i) (- 2 + 2 i) = 9 + 4 i^{2} + 2 (- 3) (2 i) - 3 [- 6 + 6 i + 2 i - 2 i^{2}]$
$= 9 - 4 - 12 i - 3 [- 6 + 8 i + 2]$
$= 9 - 4 - 12 i - 3 [8 i - 4]$
$= 9 - 4 - 12 i - 24 i + 12$
$= 17 - 36 i$

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Evaluate and write in standard form: (−3+2i)2−3(3−i)(−2+2i), where i2=−1

The correct option is B 17−36iConsider (−3+2i)2−3(3−i)(−2+2i)⇒(−3+2i)2−3(3−i)(−2+2i)=9+4i2+2(−3)(2i)−3[−6+6i+2i−2i2]=9−4−12i−3[−6+8i+2]=9−4−12i−3[8i−4]=9−4−12i−24i+12=17−36i

Evaluate and write in standard form: ${(- 3 + 2 i)}^{2} - 3 (3 - i) (- 2 + 2 i)$ , where $i^{2} = - 1$