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Calculate the imaginary number $i^k$
Answer
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$i ^{ 2019 }$
$- i$
Calculate the value
$\color{#FF6800}{ i } ^ { \color{#FF6800}{ 2019 } }$
$i ^ { 2019 } $ is calculated with exponent divided $ $
$\color{#FF6800}{ i } ^ { \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 504 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } }$
$\color{#FF6800}{ i } ^ { \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 504 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } }$
$ $ Calculate using $ i^4=1$
$\left ( \color{#FF6800}{ i } ^ { \color{#FF6800}{ 4 } } \right ) ^ { \color{#FF6800}{ 504 } } \color{#FF6800}{ i } ^ { \color{#FF6800}{ 3 } }$
$\left ( \color{#FF6800}{ i } ^ { \color{#FF6800}{ 4 } } \right ) ^ { 504 } i ^ { 3 }$
$ $ It is $ i^4=1$
$\color{#FF6800}{ 1 } ^ { 504 } i ^ { 3 }$
$\color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 504 } } i ^ { 3 }$
$ $ Calculate power $ $
$\color{#FF6800}{ 1 } i ^ { 3 }$
$1 \color{#FF6800}{ i } ^ { \color{#FF6800}{ 3 } }$
$i^2 $ is -1, so it is $ i^3=i^2\times i^1=-i$
$1 \times \left ( \color{#FF6800}{ - } \color{#FF6800}{ i } \right )$
$\color{#FF6800}{ 1 } \times \left ( - i \right )$
$ $ Multiplying any number by 1 does not change the value $ $
$- i$
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