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:

$\frac{3-4i}{2+i}(\frac{2-i}{2-i}).$

Recall that:

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

Therefore:

$\frac{3-4i}{2+i}(\frac{2-i}{2-i})=\frac{(3-4i)(2-i)}{2^2+1^2}=\frac{(3-4i)(2-i)}{5}.$

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

$\frac{6-3i-8i-4}{5}.$

Finally, simplifying the above result, we get:

$\frac{2-11i}{5}=\frac{2}{5}-\frac{11}{5}i.$

Answer:

$\begin{equation*} \frac{2}{5}-\frac{11}{5}i. \end{equation*}$