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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
If $z=\frac{7-i}{3-4 i}$, then $z^{14}=$
  • A
    $2^7$
  • B
    $2^7 i$
  • C
    $2^{14} i$
  • ✓
    $-2^7 i$
✓

Answer

Correct option: D.
$-2^7 i$
(D)
$z=\frac{7-i}{3-4 i} \times \frac{3+4 i}{3+4 i}=\frac{21+25 i+4}{16+9}$
$=\frac{25(1+ i )}{25}=(1+ i )$
$z^{14}=(1+i)^{14}=\left[(1+i)^2\right]^7=(2 i)^7=2^7 i^7=-2^7 i$

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