Precalculus 12.1a - Complex Quadratic

An example of a quadratic equation with complex coefficients. The problem is worked out and explained.

[derekowens]

Yes, that's a separate topic. There might be different ways it could be done, but I would use De'Moivre's Theorem: convert the complex number to polar form, then sqaure root the modulus, divide the angle by 2, and voila, it's done. Then convert back to rectangular form. De'Moivre's Theorem gives a quick method for raising a complex number to a power, so realizing that a square root is a power of 1/2, that should work.

[fazex]

Thanks Derek! Have an exam tomorrow about this topic.

[derekowens]

I'm using a lot of things - a graphics tablet, some screen capture software, and some video conversion software, and a headset.

As far as I understand it, finding the square root of a complex number isn't so much a general formula as it is a procedure. So I can't give you a formula. I was thinking about making a video about the procedure, though, if I can find the time.

D.O.

[girmatube]

Solve the equation: Z^2+4Z +20+¡2(A+1)=0 where A is a constant has a complex conjugate root. If one of the conjugate root is of this quadratic is Z=B+2¡, where B is areal constant, find the possible values of A. This an assignment submitted July 3o please doings my dear dear

[farlyso]

You can always write z as z = a + bi... if youre really patient.

[madeenahhassan]

thanks but where is the video you explained how to the square root of complex numbers?

[Crazytesseract]

You can program this in a Casio fx-5800P, and you get quick answers. However you explain how it is done.

[derekowens]

@abhishekutkarsh Your comment interests me. Can you elaborate on that if you have time? Thanks, DO.

[coolever]

can you please explain how you calculated the square root of 3 - 4 i into (2-i) squared? i mean is there an easier way to calculated? I understand that (2-i) squared is equal to the square root of (3 - 4i) but what if i have huge numbers under the square root? how would you calculate it? i hope my question is clear and thank you again for your videos Mr Derekowens

[Farbirge]

In simple quadratic equation, roots are points of intersection with -axis, What is the practical meaning of complex equation roots ?

[TheCaptainsWall]

I was wondering if you had any advice for me attempting the following:
z^2-8z'+16=0
Where z is a complex number and z' is it's conjugate.
Any help would be much appreciated, as I'm not sure how to use with the conjugate in there.

[ubermansh]

you probably could have used the second quadratic formula ( the one with b')

[SaiSrutiMacha-lgpc]

Wait, if i is the square root of 1, can’t we just reference it as 1? - a grade 8 student