Simplify the following - 1 - i31 - i3

(1 i)^31 i^3 #160; = (1 i)^21 + i^2 + i = 2ii = 2 ...

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Standard XII

Mathematics

Complex Numbers

Simplify the ...

Question

Simplify the following :
$\frac{(1 - i)^{3}}{1 - i^{3}}$

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Solution

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

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Simplify the following :(1−i)31−i3

(1−i)31−i3 =(1−i)21+i2+i=−2ii=−2

Simplify the following :
$\frac{(1 - i)^{3}}{1 - i^{3}}$

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