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Calculate the expression with imaginary numbers
Answer
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$\left( \dfrac{ 1-i }{ \sqrt{ 2 } } \right) ^{ 50 }$
$- i$
Calculate the $N$ square of a complex number of size $1$
$\left ( \color{#FF6800}{ \dfrac { 1 - i } { \sqrt{ 2 } } } \right ) ^ { \color{#FF6800}{ 50 } }$
$N $ square format of the special complex number has periodicity $ $
$\left ( \left ( \color{#FF6800}{ \dfrac { 1 - i } { \sqrt{ 2 } } } \right ) ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 25 } }$
$\left ( \left ( \color{#FF6800}{ \dfrac { 1 - i } { \sqrt{ 2 } } } \right ) ^ { \color{#FF6800}{ 2 } } \right ) ^ { 25 }$
$ $ It is $ \left(\dfrac { 1 - i } { \sqrt{ 2 } }\right)^2=- i$
$\left ( \color{#FF6800}{ - } \color{#FF6800}{ i } \right ) ^ { 25 }$
$\left ( \color{#FF6800}{ - } \color{#FF6800}{ i } \right ) ^ { \color{#FF6800}{ 25 } }$
$ $ Move the (-) sign forward as it does not disappear if the (-) sign is powered to an odd number of times $ $
$\color{#FF6800}{ - } i ^ { 25 }$
$- \color{#FF6800}{ i } ^ { \color{#FF6800}{ 25 } }$
$ $ Calculate $ i ^ { 25 }$
$- \color{#FF6800}{ i }$
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