qanda-logo
search-icon
Symbol
apple-logo
google-play-logo

Calculator search results

Formula
Calculate the value
Answer
circle-check-icon
expand-arrow-icon
expand-arrow-icon
expand-arrow-icon
expand-arrow-icon
expand-arrow-icon
$\dfrac{ 1 }{ i } + \dfrac{ 2 }{ i ^{ 2 } } + \dfrac{ 3 }{ i ^{ 3 } } + \dfrac{ 4 }{ i ^{ 4 } }$
$2 i + 2$
Calculate the value
$\color{#FF6800}{ \dfrac { 1 } { i } } + \dfrac { 2 } { i ^ { 2 } } + \dfrac { 3 } { i ^ { 3 } } + \dfrac { 4 } { i ^ { 4 } }$
$ $ Calculate the rationalization of the complex number $ $
$\color{#FF6800}{ \dfrac { 1 i } { - 1 } } + \dfrac { 2 } { i ^ { 2 } } + \dfrac { 3 } { i ^ { 3 } } + \dfrac { 4 } { i ^ { 4 } }$
$\dfrac { \color{#FF6800}{ 1 } i } { - 1 } + \dfrac { 2 } { i ^ { 2 } } + \dfrac { 3 } { i ^ { 3 } } + \dfrac { 4 } { i ^ { 4 } }$
$ $ Multiplying any number by 1 does not change the value $ $
$\dfrac { i } { - 1 } + \dfrac { 2 } { i ^ { 2 } } + \dfrac { 3 } { i ^ { 3 } } + \dfrac { 4 } { i ^ { 4 } }$
$\dfrac { i } { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } + \dfrac { 2 } { i ^ { 2 } } + \dfrac { 3 } { i ^ { 3 } } + \dfrac { 4 } { i ^ { 4 } }$
$ $ Move the minus sign to the front of the fraction $ $
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { i } { 1 } } + \dfrac { 2 } { i ^ { 2 } } + \dfrac { 3 } { i ^ { 3 } } + \dfrac { 4 } { i ^ { 4 } }$
$- \dfrac { i } { 1 } + \dfrac { 2 } { \color{#FF6800}{ i } ^ { \color{#FF6800}{ 2 } } } + \dfrac { 3 } { i ^ { 3 } } + \dfrac { 4 } { i ^ { 4 } }$
$ $ It is $ i^2 = -1$
$- \dfrac { i } { 1 } + \dfrac { 2 } { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } + \dfrac { 3 } { i ^ { 3 } } + \dfrac { 4 } { i ^ { 4 } }$
$- \dfrac { i } { 1 } + \dfrac { 2 } { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } + \dfrac { 3 } { i ^ { 3 } } + \dfrac { 4 } { i ^ { 4 } }$
$ $ Move the minus sign to the front of the fraction $ $
$- \dfrac { i } { 1 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 1 } } + \dfrac { 3 } { i ^ { 3 } } + \dfrac { 4 } { i ^ { 4 } }$
$- \dfrac { i } { 1 } - \dfrac { 2 } { 1 } + \dfrac { 3 } { \color{#FF6800}{ i } ^ { \color{#FF6800}{ 3 } } } + \dfrac { 4 } { i ^ { 4 } }$
$i^2 $ is -1, so it is $ i^3=i^2\times i^1=-i$
$- \dfrac { i } { 1 } - \dfrac { 2 } { 1 } + \dfrac { 3 } { \color{#FF6800}{ - } \color{#FF6800}{ i } } + \dfrac { 4 } { i ^ { 4 } }$
$- \dfrac { i } { 1 } - \dfrac { 2 } { 1 } + \color{#FF6800}{ \dfrac { 3 } { - i } } + \dfrac { 4 } { i ^ { 4 } }$
$ $ Calculate the rationalization of the complex number $ $
$- \dfrac { i } { 1 } - \dfrac { 2 } { 1 } + \color{#FF6800}{ \dfrac { 3 i } { 1 } } + \dfrac { 4 } { i ^ { 4 } }$
$- \dfrac { i } { 1 } - \dfrac { 2 } { 1 } + \dfrac { 3 i } { 1 } + \dfrac { 4 } { \color{#FF6800}{ i } ^ { \color{#FF6800}{ 4 } } }$
$ $ It is $ i^4=1$
$- \dfrac { i } { 1 } - \dfrac { 2 } { 1 } + \dfrac { 3 i } { 1 } + \dfrac { 4 } { \color{#FF6800}{ 1 } }$
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { i } { 1 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 1 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 i } { 1 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 4 } { 1 } }$
$ $ Combine the fraction with the same denominator $ $
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ i } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ i } \color{#FF6800}{ + } \color{#FF6800}{ 4 } } { 1 }$
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ i } - 2 \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ i } + 4 } { 1 }$
$ $ Calculate between similar terms $ $
$\dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ i } - 2 + 4 } { 1 }$
$\dfrac { 2 i \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } } { 1 }$
$ $ Add $ - 2 $ and $ 4$
$\dfrac { 2 i + \color{#FF6800}{ 2 } } { 1 }$
$\dfrac { 2 i + 2 } { \color{#FF6800}{ 1 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ i } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
Solution search results
Have you found the solution you wanted?
Try again
Try more features at Qanda!
Search by problem image
Ask 1:1 question to TOP class teachers
AI recommend problems and video lecture
apple-logo
google-play-logo