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Calculate the imaginary number $i^k$

Answer

$1$

It is $i^4=1$

$\color{#FF6800}{ i } ^ { \color{#FF6800}{ 4 } }$

$i ^ { 4 } $ is calculated with exponent divided $ $

$\color{#FF6800}{ i } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } }$

$ $ Calculate $ i ^ { 2 + 2 }$

$\color{#FF6800}{ i } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ i } ^ { \color{#FF6800}{ 2 } }$

$\color{#FF6800}{ i } ^ { \color{#FF6800}{ 2 } } i ^ { 2 }$

$ $ It is $ i^2 = -1$

$\color{#FF6800}{ - } \color{#FF6800}{ 1 } i ^ { 2 }$

$- 1 \color{#FF6800}{ i } ^ { \color{#FF6800}{ 2 } }$

$ $ It is $ i^2 = -1$

$- 1 \times \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$

$\color{#FF6800}{ - } 1 \times \left ( \color{#FF6800}{ - } 1 \right )$

$ $ Since negative numbers are multiplied by an even number, remove the (-) sign $ $

$1 \times 1$

$\color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 }$

$ $ Multiplying any number by 1 does not change the value $ $

$1$

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