# How do you simplify i^3 (5+i) + 7i?

Feb 18, 2016

Answer is $1 + 2 i$

#### Explanation:

To simplify ${i}^{3} \left(5 + i\right) + 7 i$, remember ${i}^{2} = - 1$ and as ${i}^{4} = {\left({i}^{2}\right)}^{2}$, ${i}^{4} = 1$.

Hence ${i}^{3} \left(5 + i\right) + 7 i$

= $5 {i}^{2} \cdot i + {i}^{4} + 7 i$

= $- 5 i + 1 + 7 i$

= $1 + 2 i$