Question

Simplify the expression $\left(1-2i\right)\left(2+i\right)$.

Short answer

The simplified value of expression is$4-3i$.

Step-by-step solution

Step 1. Write down the given information.

The given expression is $\left(1-2i\right)\left(2+i\right)$.

Step 2. Calculation.

Simplifying the given expression $\left(1-2i\right)\left(2+i\right)$.

$\begin{array}{c}\left(1-2i\right)\left(2+i\right)=1\left(2+i\right)-2i\left(2+i\right)\\ =2+i-4i-2i^2\\ =2+i-4i-2\left(-1\right)\mathrm{....}\left(\because i^2=-1\right)\\ =2-3i+2\\ =4-3i\end{array}$

Step 3. Conclusion.

The simplified value of expression is$4-3i$.