Question

3-4i/2+iCan you help me to solve this problem please

Answer 1

To solve this problem, we multiply and divide the given expression by 2-i:

`(3-4i)/(2+i)((2-i)/(2-i)).`

Recall that:

`(a+ib)(a-ib)=a^2+b^2.`

Therefore:

`(3-4i)/(2+i)((2-i)/(2-i))=((3-4i)(2-i))/(2^2+1^2)=((3-4i)(2-i))/(5).`

Finally, multiplying the factors in the numerator, we get:

`(6-3i-8i-4)/(5).`

Finally, simplifying the above result, we get:

`(2-11i)/(5)=(2)/(5)-(11)/(5)i.`

Answer:

`\begin{equation*} (2)/(5)-(11)/(5)i. \end{equation*}`