A Complex Quadratic Equation | Complex Numbers

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x^2+2x=2+4i
#PolynomialEquations #ComplexNumbers #Polynomials
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PLAYLISTS 🎵 :

[pietergeerkens]

Nice!. I managed to spot the second method right away.

[RobG]

I realize that I'm learning more when I catch mistakes before Sybermath does himself.

[kimba]

Neat. I would never have gone the second route, I saw it was a quadratic and went general solution straight off.

[rampassi]

Good Luck for introducing Mathematics Channel.

[copernic]

3rd method:
Write x as ai+b from the beginning, develop, simplify, and we get the system:
(b+1)²-a² = 3

a(b+1)=2
which leads to the solutions.

[niteshmayatwal]

What is the value of iota - 1 /iota + 1

[Qermaq]

Did it the first way, and finding the square root is often easy if you graph it. The square root of a + b1 has an argument 1/2 that of a + bi and the angle from the real axis is half. Since 3 + 4i has the legs of a PRT this is a piece of cake.

[Chitin-qyxy]

I think this is new to me cause the variables and complex numbers are combined in an expression

[walterwen]

A Complex Quadratic Equation; x^2 + 2x = 2 + 4i, Complex numbers; x = ?
x^2 + 2x = 2 + 4i, Complex numbers; x ≠ 0
x^2 + 2x + 1 = (x + 1)^2 = 2 + 4i + 1 = 3 + 4i = 4 – 1 + 4i = 2^2 + i^2 + 2(2)(i) = (2 + i)^2
x + 1 = ± (2 + i), x = – 1 ± (2 + i), x = 1 + i or x = – 3 – i
Answer check:
x = – 1 ± (2 + i); (x + 1)^2 = 3 + 4i
x^2 + 2x = (x + 1)^2 – 1 = 3 + 4i – 1 = 2 + 4i; Confirmed
Final answer:
x = 1 + i or x = – 3 – i

[moeberry]

Another video from the Master himself. Good video bro.

[Agent-cipher-]

I will first complete the square on the left and use the polar form to express the right, then just take the square roots of both sides

[mikehood]

Anyone else shouting at the screen, "JUST CANCEL THE TWOS!!!"?

[선수영-to]

일차항의 계수도 복소수로 되어있으면 어떻게 풀이해야 하나요? 예를 들면, 1차항의 계수 2x 를. (2 - 5i)x 으로 바꾸어 놓고 풀이해 주세요

[barteqw]

Substitute x=a+bi and solve system of equations:
a^2+2a-b^2=2
ab+b=b(a+1)=2
Easy to find a=1 and b=1. How about second solution? Any ideas?

[alexandermorozov]

Solve as an ordinary quadratic equation, only with complex coefficients, not?

[monishrules]

Can someone share the formula for square rooting

[Alanpoeta]

It's literally just a quadratic equation

[JohnDoe-ibds]

Excuse me, you have lost 2 in denominator, I think.