Question

The inverse of - i in the multiplicative group, {1, - 1, i , - i} is

Answer 1

Answer:

answer isssssssssssssssssss i

Answer 2

The inverse of - i in the multiplicative group {1, - 1, i , - i} is i

Given :

The multiplicative group {1, - 1, i , - i}

To find :

The inverse of - i in the multiplicative group {1, - 1, i , - i}

Solution :

Step 1 of 2 :

Find the multiplicative Identity

Let G = {1, - 1, i , - i}

Then 1 × a = a × 1 = a for all a ∈ G

So 1 is the multiplicative Identity

Step 2 of 2 :

Find the inverse of - i

Let the inverse of - i is b

Then by definition of multiplicative inverse

$\displaystyle \sf{ ( - i) \times b = b \times ( - i) = 1 }$

$\displaystyle \sf{ \implies b = \frac{1}{ - i} }$

$\displaystyle \sf{ \implies b = \frac{ - {i}^{2} }{ - i} }$

$\displaystyle \sf{ \implies b = i }$

Hence inverse of - i in the multiplicative group {1, - 1, i , - i} is i

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