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Formula
Calculate the value
$\left( \dfrac{ 1 }{ i } \right) ^{ 13 }$
$- i$
Calculate the value
$\left ( \color{#FF6800}{ \dfrac { 1 } { i } } \right ) ^ { 13 }$
 Calculate the rationalization of the complex number 
$\left ( \color{#FF6800}{ \dfrac { 1 i } { - 1 } } \right ) ^ { 13 }$
$\left ( \dfrac { \color{#FF6800}{ 1 } i } { - 1 } \right ) ^ { 13 }$
 Multiplying any number by 1 does not change the value 
$\left ( \dfrac { i } { - 1 } \right ) ^ { 13 }$
$\left ( \dfrac { i } { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } \right ) ^ { 13 }$
 Move the minus sign to the front of the fraction 
$\left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { i } { 1 } } \right ) ^ { 13 }$
$\left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { i } { 1 } } \right ) ^ { \color{#FF6800}{ 13 } }$
 Move the (-) sign forward as it does not disappear if the (-) sign is powered to an odd number of times 
$\color{#FF6800}{ - } \left ( \dfrac { i } { 1 } \right ) ^ { 13 }$
$- \left ( \color{#FF6800}{ \dfrac { i } { 1 } } \right ) ^ { \color{#FF6800}{ 13 } }$
 When raising a fraction to the power, raise the numerator and denominator each to the power 
$- \dfrac { \color{#FF6800}{ i } ^ { \color{#FF6800}{ 13 } } } { \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 13 } } }$
$- \dfrac { \color{#FF6800}{ i } ^ { \color{#FF6800}{ 13 } } } { 1 ^ { 13 } }$
 Calculate $i ^ { 13 }$
$- \dfrac { \color{#FF6800}{ i } } { 1 ^ { 13 } }$
$- \dfrac { i } { \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 13 } } }$
 Calculate power 
$- \dfrac { i } { \color{#FF6800}{ 1 } }$
$- \dfrac { i } { \color{#FF6800}{ 1 } }$
 If the denominator is 1, the denominator can be removed 
$- \color{#FF6800}{ i }$
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