Algebra 101, and some about complex numbers

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Homework Help Overview

The discussion revolves around the properties of complex numbers, specifically focusing on an equation involving the imaginary unit \(i\) and its implications in algebraic expressions. Participants are examining the transition from \(c^2 - (d^2 \cdot i^2)\) to \(c^2 + d^2\) and questioning the underlying algebraic principles.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of the imaginary unit \(i\) and its square, questioning the transition from \(c^2 - (d^2 \cdot i^2)\) to \(c^2 + d^2\). Some express confusion about their understanding of complex numbers and algebraic manipulation.

Discussion Status

The discussion is active, with participants clarifying misconceptions about complex numbers. Some have expressed gratitude for the insights provided, indicating a productive exchange of ideas. However, there remains a focus on understanding the algebraic steps involved.

Contextual Notes

Participants are grappling with the definitions and properties of complex numbers, particularly the role of \(i\) and its implications in algebraic expressions. There is an acknowledgment of initial misunderstandings regarding the nature of \(i\).

Keba
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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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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]
 
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
 
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:

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