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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers1 Mark
Question
Evaluate:
$\left(1-i+i^2\right)^{-15}$
✓

Answer

$\left(1-i+i^2\right)^{-15}=(1-i-1)^{-15}$
$=(-i)^{-15}=\frac{1}{(-i)^{15}}$
$=\frac{-1}{\left( i ^4\right)^3 \cdot i ^3}=\frac{-1}{(1)^3(- i )}$
$=\frac{1}{ i }=\frac{ i }{ i ^2}=\frac{ i }{-1}=- i $

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