Complex numbers: Solving Equations (with example)

Thanks to all supporters! They are mentioned in the credits of the video :)

#StartLearningMathematics

This video is about solving simple equations with complex numbers, also known as extracting roots from complex numbers. There is a simple algorithm and a nice visualisation for this.

I hope that this helps students, pupils and others.

(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[leNnard_]

My mind is blown, you took all my confusion and replaced it with knowledge...danke für das schöne video!

[keytoproductivity_]

do u speak german?
sprichst du deutsch?

[theblackswordsman]

This video explained waaaay better than any of my professors could have! Thank you so much!

i just have a quick question regarding this explanation. At 11:25 i do not understand why you multiplied everything by 1/3 again. Could you please explain as to why you did this? thanks

[bridgeunwort]

You said that the number of solutions we'll get is equal to the exponent. What if the exponent isn't a whole number, like a fraction, irrational number, or even imaginary/complex?

[sohaib_mer-]

god i knew going through the exponential form was the most straightforward but NO, i set
2+2i = (a+bi)^3 and god that route was so
great video keep up!

[HDitzzDH]

It probably would've been better to explain the "1/3" part in the argument from the fact that:
z = re^(iθ), thus z^3 = r^3*e^(3θ), thus 3θ = π/4 + 2π*k which means that:
θ = π/12 + 2π/3*k

[sgottk]

Awsome video, just one question

In the step where you have
z³ = √(8) * e^(i(π/4 + 2πk))

And then you take all to the 1/3 power to get

z = √(8)^(1/3) * e^(i(π/4 + 2πk)*1/3)

Over the reals, we have that for example, √x² = |x| that we can use to solve things like
x²=4
|x| = √4
x = +-√4

But is there a thing that grants that √Z² = Z(k) (meaning, the results of z in function of k) over the complex plane?

[ΘΑΝΟΣΠ-ψθ]

No one has ever taught me this way. Thank you, you are amazing!!

[tortugatech]

Great explanation! Rememebered all about complex equations i forgot since freshman year

[essayprometheus]

You are a freaking genius, i have never thought about solving complex numbers in this way. It feels like everything just makes SENSE. Thank you so much

[ishmealm]

Amazing explanation, I've never understood this so well ! Thank you very much !!

[arbenkellici]

Great explanation! Easy and clear for me, even though i am not a mathematicien Keep it up professor!

[Ransrots]

When x is equal to 0 how would you find the argument? For example this complex equation: 0 - 7776i

[tasosrokos]

Du bist der Wahnsinn...! Danke für alles!

[giorgiozannini]

Such a beautiful explanation... I love this channel

[gatlatwal]

Please help me calculate this
Given that (√3-i) is a square root of the equation Z^9+16(1+i)z^3+a+ib=0
What is the value of a and b?

[laurinwezel]

there any one else who thinks his accent, especially for words like "rewrite", is really cute?

[offthepathworks]

So you wouldn't say this is precalculus? Great video as always!

[letsgo]

How to convert it to a+bi form?
So i can plot itu

[fjorland_norsk]

dont know why but your voice makes my mind calm and relaxed. Also great video