Question

the product of i^7 and i^5

Answer 1

use the rule

x^a*x^b = x^(a+b)

to get...

i^7*i^5 = i^(7+5)

i^7*i^5 = i^(12)

Answer 2

Now if \(\Large i = \sqrt{-1}\), then...

\[\Large i = \sqrt{-1}\]

\[\Large i^2 = (\sqrt{-1})^2\]

\[\Large i^2 = -1\]

\[\Large (i^2)^6 = (-1)^6\]

\[\Large i^{2*6} = 1\]

\[\Large i^{12} = 1\]