Question

Quick Question about imaginary numbers in comment section!

Answer 1

\[Does \sqrt{3}i ^{2} equal -\sqrt{3}?\]

Answer 2

Also what i^-7 simplify to?

Answer 3

\(i^2 = -1\)

Answer 4

you need to remember that

Answer 5

and yes,
\(\large \sqrt{3} i^2 = \sqrt{3} (-1) = -\sqrt{3}\)

Answer 6

\(\large i^{-7} = \frac{1}{i^7} = ?\)

Answer 7

1/ -1 + i?

Answer 8

or 1/-i?

Answer 9

yes,

\(\large i^{-7} = \frac{1}{i^7} = \frac{1}{(i^2)^3i} = \frac{1}{(-1)^3i} = \frac{1}{-i}\)

Answer 10

but nobody likes "i" in the denominator,
so multiply top/bottom by i

Answer 11

\(\large \frac{1}{-i} \times \frac{i}{i} = \frac{i}{-i^2} = i\)

Answer 12

Are both correct though? Could it be left as is?

Answer 13

technically, both are same and correct.

Answer 14

but every one prefers "i"'s in the top oly

Answer 15

Oh okay. Thank you!!

Answer 16

think of it as rationalizing the denominator,
nobody wants radicals left in the denominator (for no particular reason ofc )

Answer 17

u wlc :)