Dividing Complex Numbers

[@TheOrganicChemistryTutor]

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[@kwagetajunior]

Find the value of 𝑥 in the equation (5𝑥 − 2)
4
3 = 16

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[@optifyoce7879]

thank you really nicely sums it up

[@Yutaro-Yoshii]

You can just invert the bottom complex number. Divide it with the magnitude and conjugate it. After that you can multiply them.

[@Yutaro-Yoshii]

This is equivalent to converting the number into polar form, inverting the magnitude, and flipping the phase.

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[@mya2174]

2:41: What if the 3 was a negative. Would you change that to a positive?

[@ojwanggeoffrey2770]

Yes

[@manloloyojosh1458]

what if the imaginary number (i) is i^3? Like for example, 4+8i/i^3?

[@survivorbest4589]

i^3 = i^2*i=-i and then do the same thing as in the video

[@mj-pt2ty]

since i^2 = -1, i^3 simplifies to -1 * i

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[@Rem__2305]

Why in the first question he only rationalize with iota and in other questions irrational iota with numbers

[@PrincessPresident]

why don't you have the conjugate for the root in the first question where you rationalized the root?

[@pettanshrimpnazunasapostle1992]

If im not wrong the conjugate is required only for complex numbers(has both real n imaginary components),the 1st radical one was only sqrt 5i(only imaginary) so no conjugate was needed

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[@3odesign]

At the 24 seconds mark in this video, how do you make the 5* i squared into -5?

[@21alia5]

i= root minus one. i squared =-1 5 i squared =-5. Hope that helps bro

[@K5310]

@@21alia5 it does! I had missed the imagery number rule :)

[@everythingkayla3103]

5:55

[@_Anna_Nass_]

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[@mr.someone5679]

I dont understand why (5i)*2 is -5

[@mr.someone5679]

Dont worry now i understand :)

[@williambudrow8036]

@@mr.someone5679 Just so anyone has the same question, I figured I'd put down why (5)i^2 = -5.
i = sqrt(-1)
sqrt(-1)^2 = -1
Effectively, i^2 = -1
Thus, (5)i^2 (where "i" is sqrt(-1), thus i^2 is -1) = (5)(-1) = -5

[@arunkrishna36108]

Do you heard of conjugate

[@StrayTm]

i don't get what complex conjugate is

[@andrewhenshaw4067]

The conjugate is the "same" number but you use the opposite sign for the imaginary part.
Conjugate of 1+i is 1-i note that the sign is the opposite
You only change the sign for the imaginary part. -3i+2 has the conjugate 2+3i NOT -3i-2.
This is because -3i+2=2-3i it's just written differently.

[@rlhm-fk8id]

3:59 : pardon, of the what? Thank you!

[@танкист108]

denominator

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@@танкист108 Thanks

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Einstein 2.0

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[@expressconverter3982]

At 3:28
ruclips.net/video/EfRRpVB62Ko/видео.html
please correct misprint in denominator. That is 9 *minus* 4

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#distributiveproperty

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