Representing this complex fracture into exponent

[nhrock3]

$$\frac{2i}{2+i}$$

i don know how to separate the complex and imaginary part of this fracture?

 

[Mentallic]

I feel stupid for actually googling fracture in mathematics to try understand this terminology. You mean fraction!

What you need to do is use the complex conjugate to rid yourself of the complex number in the denominator of this fraction.

It basically works like this: given a complex number $a+ib$ then if you multiply this by the complex conjugate $a-ib$ you get $(a+ib)(a-ib)=a^2+b^2$ which is a real number.

Don't forget to multiply the numerator by the complex conjugate also to keep things balanced