Q. 574. - Intermediate Algebra

Question

In the following exercises, multiply using the Product of Complex Conjugates Pattern. 

$\left(9-2i\right)\left(9+2i\right)$

Step-by-Step Solution

Answer

The product of given complex numbers is $85$.

Step 1. Given information.

The given complex numbers are $\left(9-2i\right)\left(9+2i\right)$

Step 2. Multiply the complex numbers.

According to the Product of Complex Conjugates,

If $a,b$ are real numbers, then

$\left(a-ib\right)\left(a+ib\right)=a^2+b^2$

Using the Product of complex conjugates, we will get

$$\begin{gathered} \left(9-2i\right)\left(9+2i\right)=9^2+2^2 \\ =81+4 \\ =85 \end{gathered}$$

 

Step 3. Conclusion.

The product of given complex numbers is $85$.