How do you simplify expressions with imaginary numbers?

Such as: ${i}^{15}$ or $\left(25 + 17 i\right) - \left(- 23 - 18 i\right)$

Apr 26, 2018

Explanation

Explanation:

${i}^{2} = - 1$ since $i = \setminus \sqrt{- 1}$
${i}^{15} = {i}^{2 \left(7\right) + 1} = {\left({i}^{2}\right)}^{7} \left(i\right) = {\left(- 1\right)}^{7} \left(i\right) = - 1 \left(i\right) = - i$

Treat the $i$ like a variable in the second case, but don't solve for it since it already has a value.
$\left(25 + 17 i\right) - \left(- 23 - 18 i\right)$
$25 + 17 i + 23 + 18 i$ (simplify signs)
$48 + 35 i$ (add like terms)