How Do Complex Number Operations Affect Results?

Click For Summary

Homework Help Overview

The discussion revolves around operations involving complex numbers, specifically focusing on expressing products in the form a+ib and addressing potential ambiguities in definitions of square roots of negative numbers.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the expression of complex number products and question the implications of different interpretations of square roots of negative numbers. There are attempts to clarify the reasoning behind specific results and the presence of ambiguity in signs.

Discussion Status

The discussion is active, with participants questioning the correctness of calculations and the definitions being used. Some guidance has been offered regarding the interpretation of square roots, but no consensus has been reached on the specific outcomes of the calculations.

Contextual Notes

There is mention of a sign ambiguity related to the definition of sqrt(-n) for n>0, which may affect the results being discussed. Additionally, participants are addressing the nature of expressions involving complex numbers and their simplifications.

Ry122
Messages
563
Reaction score
2
How do I express the following in the form a+ib?

[tex](\sqrt{-4} - 1) (\sqrt{-9})[/tex]

My attempt:
(2i - 1)(3i)
6i-3i = 3i
 
Last edited:
Physics news on Phys.org
Close, but (2i)(3i)=6i2=-6, not 6i.
 
Can you tell me why the answer -6-+3i has plus or minus 3i?

Also can you tell me the answer to (3+i)^2 - (3+i)^2
The answer I got was 0.
9+6i+i^2-9-6i-i^2=0
 
Last edited:
You have to define what you mean by sqrt(-n) for n>0. You could choose it to be either i*sqrt(n) or -i*sqrt(n). That's your sign ambiguity.
 
Ry122 said:
Can you tell me why the answer -6-+3i has plus or minus 3i?
What was that the answer to?? Surely not the (2i-1)(3i) problem you were just talking about!

Also can you tell me the answer to (3+i)^2 - (3+i)^2
The answer I got was 0.
9+6i+i^2-9-6i-i^2=0
The answer to a2- a2 is 0 no matter what a is!
 

Similar threads

Complex Number Modulus and Argument Calculations
  • · Replies 9 ·
Replies
9
Views
6K
Find roots of cubic polynomial with complex coefficient
  • · Replies 3 ·
Replies
3
Views
3K
Finding anitderivative using complex numbers and Euler
  • · Replies 5 ·
Replies
5
Views
2K
Finding root of complex equation
  • · Replies 3 ·
Replies
3
Views
2K
Complex Numbers and Euler's Identity
  • · Replies 7 ·
Replies
7
Views
2K
Partial fractions with complex linear terms
  • · Replies 8 ·
Replies
8
Views
1K
Solve a problem involving complex numbers
  • · Replies 30 ·
2
Replies
30
Views
4K
Find the complex number which satisfies the given equation
  • · Replies 6 ·
Replies
6
Views
2K
Simplifying Complex Calculation
  • · Replies 2 ·
Replies
2
Views
1K
Find the modulus and the argument of ##\dfrac{2}{(4-2i)^2}##
  • · Replies 4 ·
Replies
4
Views
2K