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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
$\frac{1-2 i}{2+i}+\frac{4-i}{3+2 i}=$
  • A
    $\frac{24}{13}+\frac{10}{13} i$
  • B
    $\frac{24}{13}-\frac{10}{13} i$
  • C
    $\frac{10}{13}+\frac{24}{13} i$
  • ✓
    $\frac{10}{13}-\frac{24}{13} i$
✓

Answer

Correct option: D.
$\frac{10}{13}-\frac{24}{13} i$
(D)
$\frac{1-2 i}{2+i}+\frac{4-i}{3+2 i}=\frac{(1-2 i)(3+2 i)+(4-i)(2+i)}{(2+i)(3+2 i)}$
$=\frac{16-2 i }{4+7 i } \times \frac{4-7 i }{4-7 i }=\frac{50-120 i }{65}=\frac{10}{13}-\frac{24}{13} i$

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