Question

Simplify

$\left(7+2i\right)\left(1-i\right)$

Short answer

The simplified value of expression is $\left(7+2i\right)\left(1-i\right)=9-5i$.

Step-by-step solution

Step 1. Given Information.

Given to simplify the expression $\left(7+2i\right)\left(1-i\right)$

Step 2. Explanation.

From the properties of complex numbers, $i^2=-1$

Using the above property,

$\begin{array}{l}\left(7+2i\right)\left(1-i\right)=7-7i+2i-2i^2\\ \left(7+2i\right)\left(1-i\right)=7-7i+2i-2\left(-1\right)\\ \left(7+2i\right)\left(1-i\right)=7-7i+2i+2\\ \left(7+2i\right)\left(1-i\right)=7+2-7i+2i\\ \left(7+2i\right)\left(1-i\right)=9-5i\end{array}$

Step 3. Conclusion.

Therefore, The simplified value of expression is $\left(7+2i\right)\left(1-i\right)=9-5i$.