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Formula
Calculate the value
Answer
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$i ^{ 50 } +i ^{ 51 } +i ^{ 52 } +i ^{ 53 }$
$0$
Calculate the value
$\color{#FF6800}{ i } ^ { \color{#FF6800}{ 50 } } + i ^ { 51 } + i ^ { 52 } + i ^ { 53 }$
$ $ Calculate $ i ^ { 50 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 1 } + i ^ { 51 } + i ^ { 52 } + i ^ { 53 }$
$- 1 + \color{#FF6800}{ i } ^ { \color{#FF6800}{ 51 } } + i ^ { 52 } + i ^ { 53 }$
$ $ Calculate $ i ^ { 51 }$
$- 1 \color{#FF6800}{ - } \color{#FF6800}{ i } + i ^ { 52 } + i ^ { 53 }$
$- 1 - i + \color{#FF6800}{ i } ^ { \color{#FF6800}{ 52 } } + i ^ { 53 }$
$ $ Calculate $ i ^ { 52 }$
$- 1 - i + \color{#FF6800}{ 1 } + i ^ { 53 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 1 } - i \color{#FF6800}{ + } \color{#FF6800}{ 1 } + i ^ { 53 }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$- i + i ^ { 53 }$
$- i + \color{#FF6800}{ i } ^ { \color{#FF6800}{ 53 } }$
$ $ Calculate $ i ^ { 53 }$
$- i + \color{#FF6800}{ i }$
$\color{#FF6800}{ - } \color{#FF6800}{ i } \color{#FF6800}{ + } \color{#FF6800}{ i }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$0$
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