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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers2 Marks
MCQ
If $iz ^3+z^2- z + i =0$, then $| z |=$
  • ✓
    1
  • B
    $0$
  • C
    2
  • D
    3
✓

Answer

Correct option: A.
1
(A)
$i z^3+z^2-z+i=0$
$\Rightarrow z ^2( iz +1)+ i ( iz +1)=0$
$\Rightarrow( iz +1)\left( z ^2+ i \right)=0$
$\Rightarrow z =\frac{-1}{ i }$ or $z ^2=- i$
$z =\frac{-1}{ i }=\frac{-1}{ i } \times \frac{ i }{ i }= i$
$\Rightarrow|z|=1$

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