# How do you simplify (3 – i^7) – 2(i^6 – 5i)?

Mar 21, 2016

You may change any ${i}^{2} = - 1$

#### Explanation:

$= \left(3 - {i}^{2} \cdot {i}^{2} \cdot {i}^{2} \cdot i\right) - 2 \left({i}^{2} \cdot {i}^{2} \cdot {i}^{2} - 5 i\right)$
$= \left[3 - \left(- 1\right) \left(- 1\right) \left(- 1\right) \cdot i\right] - 2 \left[\left(- 1\right) \left(- 1\right) \left(- 1\right) - 5 i\right]$

And if you keep good track of the $- 1$'s you get:
$= \left(3 + i\right) - 2 \left(- 1 - 5 i\right)$
$= 3 + i + 2 + 10 i$
$= 3 + 2 + i + 10 i$
$= 5 + 11 i$