Question

If G = {1, –1, i, –i}is a group under multiplication, then inverse of – i is:

Answer 1

Answer:

G= {1, -1, -I, I}

Given G is a group.Therefore the order of each element of multiplicative group is

Group generated by 1 is {1}, hence order of 1 is 1.

Group generated by -1 is {-1, 1}, hence order of -1 is 2

Group generated by i is {1,-1,i,-i}, hence order of i is 4

Group generated by -i is {1,-1,i,-i}, hence order of -i is 4

Generator of group is i and -i.

Answer 2

Answer:

The answer is "i"

Concept:

Discrete mathematics. The inverse of -i is i

Step-by-step explanation:

$G=\left\{1, i_{1}-1,-i\right\} . \\Inverse of 1 is 1\\Inverse of i=-i \\Inverse of -1=-1 \\Inverse of -i=i \\ \begin{aligned}&a \times a^{-1}=l(identity \ element \ i.e.,1) \\&1 * 1=1 \\&i *-i=-i^{2}=1 \\&-1 *-1=1 \\&-i * i=1\end{aligned}$

By applying the conditions using identity element and inverse method, we will get the above answers.

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