Because i equals the root of -1 and so when you square this you get -1... -1 multiplied by b squared gives - b squared. Take a look at my early videos on complex numbers to see these basic results for squaring, cubing etc for values of i.
If b isn't real and has an i component, the final answer would be a+bi^2. Which is equal to a-b, and there would be no imaginery parts in the final answer, thus it would not be a complex number[
+faiza anwar At 6.44 I said that b was a real number. It is not an imaginary number. 3i is imaginary but the 3 is real. So bi is imaginary but b is a real number. I hope that makes sense.
Because i equals the root of -1 and so when you square this you get -1... -1 multiplied by b squared gives - b squared. Take a look at my early videos on complex numbers to see these basic results for squaring, cubing etc for values of i.
I'm not sure. I just wanted an explanation on how to factorise those quartic equations that you did in this video
Use u substitution. Substitute b^2 for u and it becomes a quadratic. Solve for u. Once solved for u, replace u again with b^2 and then solve for b.
@@AliShaikh_744 Thank you brother 😊❤️, I really appreciate it, I now understand
@@emmydee408 Glad I was able to help😁
Thank you that was really helpful. Excellently explained, thanks again.
How can I pay you money?
you can now donate to him! please consider if possible though it's completely understandable if you cant due to the pandemic :)
Thank you man may god bless u😊
why solution for square root of y must be real number ? 6:35 and 11:30
If b isn't real and has an i component, the final answer would be a+bi^2. Which is equal to a-b, and there would be no imaginery parts in the final answer, thus it would not be a complex number[
@@junaidwali8938 you're about 3 years and 6 months late
... time travel@@radheypatel9622
@@radheypatel9622 better late than never😅
i like the way u interpret the question
you are a saviour 🙏🙏🙏
God bless you
why does b have to be a real value 6:40?
It will yield the same result by considering only b real. The a and b will only be swapped
If b is not real then it would make a+bi into just a+b (as i x i is real) and so it won't make it correct statement
Safe Rehman ah ok
Thanks mate
No problem
Do you have a video up on how to factorise quartic equations?
Thanks
Can't believe this was uploaded when i was 10 years old
Sir, may I know at the beginning part, how did you make that ...+b squared i squared reduced to -b squared?
I know it's been 9 years, but seriously? That was the most difficult part to understand?
It's because it's (bi)² so b²i² i²=-1 so it's b²×-1 so -b²
There are 2 types of people lmao
i needed this
(a+bi)^2
=(a^2-b^2)+2abi
7-24i
So .. ab=-12 and
(a-b)(a+b)=7
a=-4, b=3 is a solution, as is a=4, b=-3.
i.e. -4+3i, 4-3i.
Thank you very much!
Quality video. Thanks for the help.
Cheers
+faiza anwar At 6.44 I said that b was a real number. It is not an imaginary number. 3i is imaginary but the 3 is real. So bi is imaginary but b is a real number. I hope that makes sense.
b is a real number. For example 2i is an imaginary number but the 2 is real
Do you mean ones with complex roots?
but if you substitute B= -5, +5 into the first equation (a^2-b^2= -21) you would only get a=2 right?
You sir are a legend thank you so much
Best wishes - thanks for your support.
Thanks a lot
Very helpful.
... if I may ask... why isn't b = +/- 2i one of the solutions ?
because in this case, B is the co-efficient of the imaginary number and +/- 2 was gained by solving for the real number
e^ipi = -1, i^2ipi = 1, 4(e^2ipi) = 4
😭😭😭you saved me
Super
Sorry, my brother logged into my e-mail account and replied to this. Rest assured, I understood it. Well played sir.
if i want to find the square root of 1+root of 2 for example can i use a similar method?
Yes
Oh okay, and now i noticed i made a typo in the second statement :O that i should be an e....
nice
Sugene Kim approved
-(i^2) st.
Why did the sign not change when the 21b^2 switched sides
did you ever figure this out haha
Because it didn't switch sides, he added b⁴ and and subtracted 100 to make it 0=b⁴-21b²-100 but just wrote it the other way round as b⁴-21b²-100
but if you use b=12/a, the answer is ±(4+3i) instead of ±(4-3i)
does it matter?
:) thanks
b = -12/a not 12/a
How is that a negative B squared
Haha it seems so! I didn't bother to look, I read the first comment anyway.
gud
what if there was a "z" in the complex equation ?
Z is not part of a complex equation z IS a complex equation
*first ;)
f
???
Or we can use polar forms
Thank you!