How to simplify 1/i (Complex Numbers)

Steps on how to simplify 1/i to equal -i

This tutorial covers how to simplify the complex number 1/i by using a technique similar to multiplying by the complex conjugate to make the denominator a real number.

Note that i=sqrt(-1) in this example.

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Music by Adrian von Ziegler

[ryanhunt]

This is the most peaceful math tutorial I've ever watched

[jarvis]

I was so confused and searching for the answers everywhere. I was like how can it be. But now I am so clear thank you and plz make more videos

[Ryuusei]

god ive been looking for this answer all over the place, thank you.

[nadirbaitsaleem]

Nice music choice and very simple explanation. Thanks!

[clairezwicker]

Thank you, for this, video. This video, has saved me, several times. Thank you, bb.

[MRSoefeldt]

Yeah it has to be this way. Look at the unit circle in the complex plane. i^2=-1, i^1=i, i^0=1, i^-1=-i.... and ofc then i^-2=-1, i^-3=i....

[andersongonzalez]

Thank you, bro. You deserve the everyone's love ❤
Sorry for my english.

[lukasjetu]

i¹=√(-1)
i²=-1
i³=-i
i⁴=1
this repeats indefinitely,
so 1/i, we use exponents to get i^(-1), we add 4 to the exponent and now we see i^(3) and that is -i,

[sukirii]

but what if:
i² = -1
1/i² = -1
so i² = 1/i²
then i² = i^(-2)
by taking the srq root i = i(^-1)
leading to i = 1/i

[linachandulaljani]

You zeroed out the crux of the matter. Thank you very much.

[gabrialpetersen]

I get skyrim vibes from this music..I like it.

[SequinBrain]

so, is this the only time something changes its sign when simplifying?

[koneefive]

thanks man, wanted to now why that happens :D

[TralalaCookies]

thank you, you wonderful person <3 all is clear, professors just said "yup its -1" and moved on

[righthomosphere]

Please help I don't understand why I'm wrong!
1/i
Why is this not correct?

[techgenius]

i found i because if we get squre of 1/i it is equals 1/-1 its equals -1 than i get sqrt it and get i so 1/i = i and also equals -i (is it?)

[thestovietunion]

1/i = 1/sqrt(-1) = sqrt(1)/sqrt(-1) = sqrt(1/-1) = sqrt(-1) = i
What is wrong with this?

[Quassarr]

Thank you very much sir/ma'am
I was stuck here ...Thank you for your help ❤

[jjk]

I am one with my myself and with nature

[agartroby]

what about this-
1/i=1/√-1, √(1/-1)=√-1=i (may be i am wrong)