Solving Complex Expressions: 1/z^2 & 1/z^3

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Homework Help Overview

The discussion revolves around complex numbers, specifically evaluating expressions involving powers of a complex number, z = 1 + 2i. The original poster seeks to find 1/z^2 and 1/z^3.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster considers using the conjugate to simplify the expressions. Some participants suggest calculating 1/z first as an alternative approach. There is also a discussion about the notation used for the expressions, particularly the distinction between 1/z^2 and (1/z)^2.

Discussion Status

The conversation includes attempts to clarify the notation and understanding of the problem. Participants are engaging with each other's ideas, and there is a recognition of confusion regarding the expressions involved. No consensus has been reached, but there are multiple interpretations being explored.

Contextual Notes

Participants express concerns about the appropriateness of the thread's placement and the clarity of their own contributions, indicating a learning environment where assumptions and definitions are being questioned.

ENGR_student
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Hello I'm studying complex numbers for class and the question is stated as:
Let z=1+2i
Find:
a) 1/z^2
b) 1/z^3

I was thinking just to multiply by the conjugate (1-2i)^2 for (a) and similarly for (b).
Would that be correct in solving it?
 
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You can do that, right.
Alternatively, calculate 1/z first, and then calculate powers of that.

As this looks like homework, I moved your thread.
 
Oh thank you!
I apologize if I put it in the wrong thread!
 
ENGR_student said:
Oh thank you!
I apologize if I put it in the wrong thread!
Firstly, let's establish what you are actually asking.

For example, the way you wrote it, 1/z^2 = [itex]\frac{1}{z^2}[/itex], NOT [itex](\frac{1}{z})^2[/itex]

EDIT: Please ignore. Complete brain-fart by me there! :redface:
 
Last edited:
oay said:
For example, the way you wrote it, 1/z^2 = [itex]\frac{1}{z^2}[/itex], NOT [itex](\frac{1}{z})^2[/itex]
Where is the difference?
 
mfb said:
Where is the difference?
Thanks. I simply cannot believe what I wrote in my previous post.

I blame lack of sleep...:zzz:
 
Surely there must be some way to completely delete a post so that those of us who post a really stupid idea can pretend it never happened!?
 

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