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Calculate the expression with imaginary numbers
Answer
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$- 4$
Expand of the Nth square expression regarding a complex number
$\left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ i } \right ) ^ { \color{#FF6800}{ 4 } }$
$ $ Bind only the least squares separately to form a monomial from a binomial containing imaginary numbers $ $
$\left ( \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ i } \right ) ^ { \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$\left ( \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ i } \right ) ^ { \color{#FF6800}{ 2 } } \right ) ^ { 2 }$
$ $ Expand the square of a binomial including imaginary numbers $ $
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ i } \right ) ^ { 2 }$
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ i } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Solve the power $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ i } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } i ^ { 2 }$
$ $ Calculate power $ $
$\color{#FF6800}{ 4 } i ^ { 2 }$
$4 \color{#FF6800}{ i } ^ { \color{#FF6800}{ 2 } }$
$ $ It is $ i^2 = -1$
$4 \times \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
$\color{#FF6800}{ 4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
$ $ Multiply $ 4 $ and $ - 1$
$\color{#FF6800}{ - } \color{#FF6800}{ 4 }$
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