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Formula
Calculate the value
$i ^{ 1003 } + \left( -i \right) ^{ 1003 }$
$0$
Calculate the value
$\color{#FF6800}{ i } ^ { \color{#FF6800}{ 1003 } } + \left ( - i \right ) ^ { 1003 }$
 Calculate $i ^ { 1003 }$
$\color{#FF6800}{ - } \color{#FF6800}{ i } + \left ( - i \right ) ^ { 1003 }$
$- i + \left ( \color{#FF6800}{ - } \color{#FF6800}{ i } \right ) ^ { \color{#FF6800}{ 1003 } }$
 Move the (-) sign forward as it does not disappear if the (-) sign is powered to an odd number of times 
$- i \color{#FF6800}{ - } i ^ { 1003 }$
$- i - \color{#FF6800}{ i } ^ { \color{#FF6800}{ 1003 } }$
 Calculate $i ^ { 1003 }$
$- i - \left ( \color{#FF6800}{ - } \color{#FF6800}{ i } \right )$
$- i \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } i \right )$
 Simplify Minus 
$- i + i$
$\color{#FF6800}{ - } \color{#FF6800}{ i } \color{#FF6800}{ + } \color{#FF6800}{ i }$
 Remove the two numbers if the values are the same and the signs are different 
$0$
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