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Calculate the value
Answer
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$\left( \dfrac{ \sqrt{ 2 } }{ 1+i } \right) ^{ 2 }$
$- i$
Calculate the value
$\left ( \color{#FF6800}{ \dfrac { \sqrt{ 2 } } { 1 + i } } \right ) ^ { 2 }$
$ $ Calculate the rationalization of the complex number $ $
$\left ( \color{#FF6800}{ \dfrac { \sqrt{ 2 } - \sqrt{ 2 } i } { 2 } } \right ) ^ { 2 }$
$\left ( \color{#FF6800}{ \dfrac { \sqrt{ 2 } - \sqrt{ 2 } i } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ When raising a fraction to the power, raise the numerator and denominator each to the power $ $
$\dfrac { \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ i } \right ) ^ { \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } }$
$\dfrac { \left ( \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ i } \right ) ^ { \color{#FF6800}{ 2 } } } { 2 ^ { 2 } }$
$ $ Expand the square of a binomial including imaginary numbers $ $
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ i } } { 2 ^ { 2 } }$
$\dfrac { - 4 i } { \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$\dfrac { - 4 i } { \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ \dfrac { - 4 i } { 4 } }$
$ $ Reduce the fraction $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 1 } \color{#FF6800}{ i }$
$\color{#FF6800}{ - } \color{#FF6800}{ 1 } i$
$ $ Multiplying any number by 1 does not change the value $ $
$- i$
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