# How do you simplify (3 + 4i)(3 - 4i)?

Feb 12, 2016

25

#### Explanation:

Given:$\text{ } \left(3 + 4 i\right) \left(3 - 4 i\right)$

I notice that this is our good old friend of

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

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Write as:$\text{ } {3}^{2} - {\left(4 i\right)}^{2}$

$= 9 - \left(16 {i}^{2}\right)$

But $\text{ } {i}^{2} = - 1$ giving:

$= 9 + 16 = 25$