Re(-2+3i) Real part =−2 Imaginary part=3 A: −2=−2 B: −6−2i3+i=−6−2i3+i×3−i3−i=(−6−2i)(3−i)32−i2 =−18+6i−6i+2i29−(−1)=−18+2(−1)9+1 =−18−210=−2010=−2 C: −4−(−2)=−4+2=−2 D: −2+i.o=−2+0=−2

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$Re (- 2 + 3 i)$ is

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- 2

\frac{- 6 - 2 i}{3 + i}

- 4 - (- 2)

- 2 + i . o

answer is D.

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Detailed Solution

Re (- 2 + 3 i)

$Real part = - 2$

$Imaginary part=3$

A: $- 2 = - 2$

B: $\frac{- 6 - 2 i}{3 + i} = \frac{- 6 - 2 i}{3 + i} \times \frac{3 - i}{3 - i} = \frac{(- 6 - 2 i) (3 - i)}{3^{2} - i^{2}}$

$= \frac{- 18 + 6 i - 6 i + 2 i^{2}}{9 - (- 1)} = \frac{- 18 + 2 (- 1)}{9 + 1}$

$= \frac{- 18 - 2}{10} = \frac{- 20}{10} = - 2$

C: $- 4 - (- 2) = - 4 + 2 = - 2$

D: $- 2 + i . o = - 2 + 0 = - 2$

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