# How do you write the expression i ^-18 in the standard form a+ bi?

Feb 12, 2015

${i}^{- 18} = - 1$
so $a + b i$ becomes
$\left(- 1\right) + \left(0\right) i$

To see that ${i}^{- 18} = - 1$
note that
${i}^{1} = \sqrt{- 1}$
${i}^{0} = 1$
${i}^{-} 1 = \frac{1}{\sqrt{- 1}}$
${i}^{-} 2 = \frac{1}{- 1} = - 1$

${i}^{-} 18 = {\left({i}^{-} 2\right)}^{9} = {\left(- 1\right)}^{9} = - 1$