We know that #160; i ^ 2 = 1 ∴ #160; #160; i ^ 3 = i ^ 2 .i= 1× i= i amp; #160; #160; 1 i = 1× 1 i = i ^ 2 × i ^ 2 i =i× ...

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Properties of Iota

i3=1i=1i×ii=-...

Question

$i^{3} = \frac{1}{i} = \frac{1}{i} \times \frac{i}{i} = \frac{- i}{1} = - i$

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Solution

We know that $i^{2} = - 1$
$∴$ $i^{3} = i^{2} . i = - 1 \times i = - i$
& $\frac{1}{i} = \frac{- 1 \times - 1}{i} = \frac{i^{2} \times i^{2}}{i} = i \times i^{2} = - i$
$∴$ $i^{3} = \frac{1}{i} = - i$

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