Question

Please explain!

What is the multiplicative inverse of 3i?

Answer 1

what do you think

Answer 2

oh by the way is that \[3i \]

Answer 3

Yes, it's 3i

Answer 4

recall that if 1/a is a multiplicative inverse of a
then \[a\times\frac{1}{a}=1\]

Answer 5

3/i

Answer 6

so can you find such number that satisfies this condition

Answer 7

Answer is actually -i/3, but how do I figure that out?

Answer 8

because technically its 3 times i so its 3i, so the multiplicative inverse of 3i is division, so its 3 over i

Answer 9

i would agree with that answer -i/3
see the condition i wrote and reflect on it

Answer 10

@Saisuke<3 i stands for imaginary, it's not just a variable

Answer 11

thing of 3i as a
1/a is the inverse of a then we should have 1/3i yes?

Answer 12

think*

Answer 13

But that wouldn't make any sense as the answer is -i/3

Answer 14

well it makes perfect sense actually
if 1/3i is the inverse of 3i
you just need to do some rationalizing the denominator to get rid of i

Answer 15

@Albert0898
-i/3 and 1/3i are the same number, like @xapproachesinfinity said.
We prefer the first because we don't like i in the denominator, just like we write
\(\dfrac{\sqrt 2}{2}\) instead of \(\dfrac{1}{\sqrt 2}\)
So by multiplying 1/3i by i top and bottom, we get i/(3(-1)=-i/3

Answer 16

Ah, now I get it. I knew how to the inverse and I got 1/3i and that wasn't a choice. Thank you all!

Answer 17

np!