The correct option is D 1013 2413i 1 2i/2+1 +4 1/(3+2i) (1 2i)(3+2i)+(4 i)(2+i)/(2+i)(3+2i) 3+2i 6i+4+8+4i 2i+1/6+4i+3i 2 3 4i+12+2i+1/ ...

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Addition of Rational Numbers

1-2i2+i+4-i3+...

Question

$\frac{1 - 2 i}{2 + i} + \frac{4 - i}{3 + 2 i} =$

\frac{24}{13} + \frac{11}{13} i

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\frac{24}{13} - \frac{11}{13} i

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\frac{10}{13} + \frac{24}{13} i

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\frac{10}{13} - \frac{24}{13} i

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Solution

The correct option is D $\frac{10}{13} - \frac{24}{13} i$
$\frac{1 - 2 i}{2 + 1} + \frac{4 - 1}{(3 + 2 i)}$

$\frac{(1 - 2 i) (3 + 2 i) + (4 - i) (2 + i)}{(2 + i) (3 + 2 i)}$

$\frac{3 + 2 i - 6 i + 4 + 8 + 4 i - 2 i + 1}{6 + 4 i + 3 i - 2}$

$\frac{3 - 4 i + 12 + 2 i + 1}{6 + 7 i - 2}$

$\frac{- 2 i + 16}{7 i + 4}$

$\frac{16 - 2 i}{4 + 7 i} \times \frac{(4 - 7 i)}{4 - 7 i}$

$\frac{64 - 112 i - 8 i - 14}{16 + 49}$

$\frac{50 - 120 i}{65}$

$= \frac{10 - 24 i}{13}$

$= \frac{10}{13} - \frac{24 i}{13}$

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1−2i2+i+4−i3+2i=

The correct option is D 1013−2413i1−2i2+1+4−1(3+2i)(1−2i)(3+2i)+(4−i)(2+i)(2+i)(3+2i)3+2i−6i+4+8+4i−2i+16+4i+3i−23−4i+12+2i+16+7i−2−2i+167i+416−2i4+7i×(4−7i)4−7i64−112i−8i−1416+4950−120i65=10−24i13=1013−24i13

$\frac{1 - 2 i}{2 + i} + \frac{4 - i}{3 + 2 i} =$