# How do you multiply (1+i)(1-i)?

Jan 31, 2016

Just as you would multiply any similar set of brackets: FOIL (first, outers, inners, lasts). In this case this totals 2.

#### Explanation:

Multiplying through using the FOIL approach:

$\left(1 + i\right) \left(1 - i\right) = \left(1 \cdot 1\right) + \left(1 \cdot - i\right) + \left(i \cdot 1\right) + \left(i \cdot - i\right)$
$= \left(1 + i - i - {i}^{2}\right)$ but remember, since $i = \sqrt{- 1}$, ${i}^{2} = - 1$.
$= 1 + 1 = 2$

in this case, the answer is a real number.