Write as sum of real and imaginary part

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Homework Help Overview

The discussion revolves around expressing the complex fraction 1/(a+ib) as a sum of its real and imaginary parts, focusing on the manipulation of complex numbers.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use the complex conjugate to simplify the expression and seeks guidance on the next steps. Other participants discuss the implications of the approach and question the completeness of the solution for a learner.

Discussion Status

Some participants have provided encouragement regarding the use of the complex conjugate, while others express concern about the adequacy of the explanation for someone new to the topic. Multiple interpretations of the problem's requirements are being explored.

Contextual Notes

There is an indication that the original poster is a student learning about complex numbers, which may affect how the solution is approached and understood.

greisen
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Hi,

I have to write the 1/(a+ib) as a sum of a real part and an imaginary part.

I was thinking of using the complex conjugate (a-ib) and multiply with this

(a-ib) / (a^2 + b^2)

I am a little bit lost on what to do next - any help appreciated thanks in advance

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greisen said:
(a-ib) / (a^2 + b^2)

I am a little bit lost on what to do next - any help appreciated thanks in advance

Do you know how to write (x+y)/z as the sum of two fractions?
 
greisen said:
(a-ib) / (a^2 + b^2)

Hi greisen! :smile:

You've done it!

That is the solution! :smile:
 
tiny-tim said:
That is the solution!

Not for a student who is just learning complex numbers. He won't get full marks if he leaves it at that.
 

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