Question

Perform the following operations on
these complex numbers.
2+i
____
2-i

Answer 1

Answer:
`3/5+4/5i`

Step-by-step explanation: Great Question! With square roots or imaginary numbers in fraction form, multiplying by the conjugate, proves to be an effective method of simplification.

Let's break down how to simplify this:

We are given:
`(2+i)/(2-i)`

We multiply by the conjugate of the denominator(which is the numerator), and distribute:

`(2+i)/(2-i) * (2+i)/(2+i)` =
`(4i+3)/(5)`

Now, separate them into real and imaginary terms as denoted by a+bi where a is the real component and b is the imaginary component:

`3/5+4/5i`

That's it!