# How do you simplify 5i^4 + 3i^2 + 4i^7 - 4?

Nov 17, 2015

$- 2 - 4 i$

#### Explanation:

We may use the fact that ${i}^{2} = - 1$ to write the following

$5 {i}^{4} + 3 {i}^{2} + 4 {i}^{7} - 4 = 5 \left({i}^{2} \cdot {i}^{2}\right) + 3 {i}^{2} + 4 \left({i}^{2} \cdot {i}^{2} \cdot {i}^{2} \cdot i\right) - 4$

$= 5 - 3 - 4 i - 4$

$= - 2 - 4 i$