Write as sum of real and imaginary part

In summary, the conversation discusses how to write 1/(a+ib) as a sum of a real part and an imaginary part, and suggests using the complex conjugate (a-ib) to solve it. The conversation also mentions writing (x+y)/z as the sum of two fractions and the importance of providing a complete solution for a student learning complex numbers.
  • #1
greisen
76
0
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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  • #2
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?
 
  • #3
greisen said:
(a-ib) / (a^2 + b^2)

Hi greisen! :smile:

You've done it!

That is the solution! :smile:
 
  • #4
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.
 

1. What does it mean to write a number as the sum of a real and imaginary part?

Writing a number as the sum of a real and imaginary part is a way to express a complex number in the form of a + bi, where 'a' represents the real part and 'bi' represents the imaginary part. This notation is used to represent numbers that involve both a real and imaginary component, such as the square root of a negative number.

2. How do you determine the real and imaginary parts of a complex number?

To determine the real and imaginary parts of a complex number, you can use the formula a + bi, where 'a' is the real part and 'bi' is the imaginary part. The real part is the coefficient of the term without the 'i', and the imaginary part is the coefficient of the term with the 'i'.

3. Can a complex number have a real part of 0?

Yes, a complex number can have a real part of 0. In this case, the complex number would be written as 0 + bi, where 'bi' represents the imaginary part of the number.

4. How can you add or subtract complex numbers written as the sum of a real and imaginary part?

To add or subtract complex numbers written as the sum of a real and imaginary part, you can simply combine the real parts and the imaginary parts separately. For example, to add (3 + 2i) and (2 + 4i), you would add 3 and 2 for the real part, and 2i and 4i for the imaginary part, giving you a final result of 5 + 6i.

5. Why is it useful to write a complex number as the sum of a real and imaginary part?

Writing a complex number as the sum of a real and imaginary part allows for easier manipulation and calculation of complex numbers. It also allows for a more visual representation of the number, making it easier to understand and work with in mathematical equations.

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