Write as sum of real and imaginary part

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To express 1/(a+ib) as a sum of real and imaginary parts, the complex conjugate (a-ib) is used to multiply the numerator and denominator, resulting in (a-ib)/(a^2 + b^2). The next step involves separating the resulting fraction into its real and imaginary components. While some participants affirm the method is correct, concerns are raised about its clarity for beginners in complex numbers. It is emphasized that further breakdown is necessary for students to fully understand and achieve full marks.
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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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