Question

Provide an example of two expressions that are conjugates of each other.


Rationalize the following expression:
6/5+i

Answer 1

1 - i and 1 + i are complex conjugates.
The standard method to solve your problem is to multiply top and bottom by the complex conjugate of what's on the bottom. Can you do that?

Answer 2

so would i multiply 6*1-i/5*1+i

Answer 3

No, 1 - i and 1 + i is just one example. In your problem, the complex conjugate of 5 + i is 5 - i.

Answer 4

Can you multiply (5+i)(5-i) ?

Answer 5

would it be 26 ?

Answer 6

Yes. - i times i = 1
So now what is the top? What is 6 (5 - i)

Answer 7

30-6i

Answer 8

So now we have (30-6i) / 26, which can be simplified a bit.

Answer 9

And that's the whole point of complex conjugates here, multiplying by it makes the i terms in the denominator go away.

Answer 10

oh i get it now Thank You.

Answer 11

yw