Q. 573. - Intermediate Algebra

Question

In the following exercises, multiply using the Product of Binomial Squares Pattern.

Step-by-Step Solution

Answer

Square of the given complex number is ${\left(-2-3i\right)}^2$.

Step 1. Given information.

The given complex number is ${\left(-2-3i\right)}^2$.

Step 2. Multiply the complex number.

According to the Binomial Squares Pattern,

${\left(a+b\right)}^2=a^2+2ab+b^2$

Use this concept, we will get 

$$\begin{gathered} {\left(-2-3i\right)}^2={\left(-2\right)}^2+2·\left(-2\right)·\left(-3i\right)+{\left(-3i\right)}^2 \\ =4+12i+9i^2 \end{gathered}$$

We know that, 

$i^2=-1$

then 

$$\begin{gathered} {\left(-2-3i\right)}^2=4+12i+9\left(-1\right) \\ =4+12i-9 \\ =-5+12i \end{gathered}$$

Step 3. Conclusion.

Therefore, the multiplication of the given complex number is $-5+12i$.