# Useful Tables (Taylor & Maclaurin Series)

Negative 1 Exponentiated Imaginary Numbers Exponentiated
${ \left( -1 \right) }^{ 0 }=1$ $\sqrt { -1 } =i$
${ \left( -1 \right) }^{ 1 }=-1$ $i\cdot i={ i }^{ 2 }=-1$
${ \left( -1 \right) }^{ 2 }=1$ ${ i }^{ 3 }={ i }^{ 2 }\cdot i=-i$
${ \left( -1 \right) }^{ 3 }=-1$ ${ i }^{ 4 }={ i }^{ 3 }\cdot i=-i\cdot i=-{ i }^{ 2 }=1$
${ \left( -1 \right) }^{ 4 }=1$ ${ i }^{ 5 }={ i }^{ 4 }\cdot i=i$
${ \left( -1 \right) }^{ 5 }=-1$ ${ i }^{ 6 }={ i }^{ 5 }\cdot i=i\cdot i={ i }^{ 2 }=-1$
${ \left( -1 \right) }^{ 6 }=1$ ${ i }^{ 7 }={ i }^{ 6 }\cdot i=-i$
${ \left( -1 \right) }^{ 7 }=-1$ ${ i }^{ 8 }={ i }^{ 7 }\cdot i=-i\cdot i=-{ i }^{ 2 }=1$
${ \left( -1 \right) }^{ 8 }=1$ ${ i }^{ 9 }={ i }^{ 8 }\cdot i=i$
${ \left( -1 \right) }^{ 9 }=-1$ ${ i }^{ 10 }={ i }^{ 9 }\cdot i={ i }^{ 2 }=-1$
${ \left( -1 \right) }^{ 10 }=1$ ${ i }^{ 11 }={ i }^{ 10 }\cdot i=-i$