# How do you multiply (3-5i)(3+5i)?

May 25, 2018

Answer: $34$

#### Explanation:

Note that the expression is in the difference of squares pattern $\left(a - b\right) \left(a + b\right)$, which is equal to ${a}^{2} - {b}^{2}$

By applying this formula, we have:

$\left(3 - 5 i\right) \left(3 + 5 i\right) = {3}^{2} - {\left(5 i\right)}^{2}$

$= 9 - {5}^{2} \cdot {i}^{2}$

Noting that ${i}^{2} = - 1$,

$= 9 - \left(- 25\right)$

$= 9 + 25$

$= 34$