How do you simplify 2i^5(i-7i^15) ?

Mar 3, 2016

The value of this expression is $- 16$

Explanation:

$2 {i}^{5} \cdot \left(i - 7 {i}^{15}\right) = 2 i \cdot \left(i - 7 {i}^{3}\right) = 2 i \cdot \left(i - 7 i \cdot {i}^{2}\right) =$
$= 2 i \cdot \left(i + 7 i\right) = 2 i \cdot 8 i = 16 {i}^{2} = - 16$

In the calculations I used the following properties of imaginary unit:

• ${i}^{2} = - 1$

• ${i}^{4} = 1$