Algebra 101, and some about complex numbers

In summary, the conversation discusses a confusion regarding a complex number equation on YouTube. The user initially thought that i was equal to -1, but the correct understanding is that i is the square root of -1. The equation is then simplified to c^2-(d^2*i^2) = c^2+d^2 to properly represent complex numbers. The user thanks the other person for correcting their misunderstanding.
  • #1
Keba
17
0

Homework Statement


I was looking up complex numbers and the guy on YouTube made something similar to this equation:
i=-1
c^2-(d^2*i^2) = c^2+d^2

( - 2:55)

Homework Equations


I do not understand why it is "c^2+d^2" and not "c^2-d^2"
I would like a detailed explanation, as I might have misunderstood algebra somehow

The Attempt at a Solution


I would do this to find a solution
c^2-(d^2*i^2)
c^2-(d^2*(-1)^2)
c^2-(d^2*1)
c^2-d^2
 
Last edited by a moderator:
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  • #2
The general form of a complex nr is ;a+bi, where i is the imaginary.

it is the square root of negative one, that is:

[tex]\sqrt{-1}=i=>i^2=-1[/tex] now going back to what u have there

[tex]c^2-(d^2i^2)=c^2-(d^2(-1))=c^2+d^2[/tex]
 
  • #3
I see, so my problem wasn't with algebra but with my understanding of complex numbers.
Then it makes perfect sense! I thank you good sir =P
 
  • #4
Keba said:

Homework Statement


I was looking up complex numbers and the guy on YouTube made something similar to this equation:
i=-1
Here was your error. i is NOT -1. Its square is -1: i2= -1.

c^2-(d^2*i^2) = c^2+d^2

( - 2:55)

Homework Equations


I do not understand why it is "c^2+d^2" and not "c^2-d^2"
I would like a detailed explanation, as I might have misunderstood algebra somehow

The Attempt at a Solution


I would do this to find a solution
c^2-(d^2*i^2)
c^2-(d^2*(-1)^2)
c^2-(d^2*1)
c^2-d^2
 
Last edited by a moderator:

1. What is Algebra 101?

Algebra 101 is an introductory course in mathematics that covers basic algebraic concepts and techniques, such as solving equations, graphing lines and functions, and manipulating algebraic expressions.

2. Why is Algebra 101 important?

Algebra 101 is important because it provides the foundation for more advanced mathematical concepts and real-world applications. It also helps develop critical thinking and problem-solving skills.

3. What are complex numbers?

Complex numbers are numbers that contain both a real and an imaginary part. They are typically written in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit (defined as the square root of -1).

4. How are complex numbers used?

Complex numbers are used in various fields of mathematics, physics, and engineering to solve problems that involve both real and imaginary quantities. They also have practical applications in electrical engineering, signal processing, and quantum mechanics.

5. Is Algebra 101 a difficult course?

The difficulty of Algebra 101 can vary depending on the individual's background and mathematical aptitude. However, with proper study and practice, most students are able to grasp the concepts and succeed in the course.

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