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Formula
Calculate the value
$\dfrac{ 2-3i }{ 2+3i } + \dfrac{ 2+3i }{ 2-3i }$
$- \dfrac { 10 } { 13 }$
Calculate the value
$\color{#FF6800}{ \dfrac { 2 - 3 i } { 2 + 3 i } } + \dfrac { 2 + 3 i } { 2 - 3 i }$
 Calculate the rationalization of the complex number 
$\color{#FF6800}{ \dfrac { - 5 - 12 i } { 13 } } + \dfrac { 2 + 3 i } { 2 - 3 i }$
$\dfrac { - 5 - 12 i } { 13 } + \color{#FF6800}{ \dfrac { 2 + 3 i } { 2 - 3 i } }$
 Calculate the rationalization of the complex number 
$\dfrac { - 5 - 12 i } { 13 } + \color{#FF6800}{ \dfrac { - 5 + 12 i } { 13 } }$
$\color{#FF6800}{ \dfrac { - 5 - 12 i } { 13 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { - 5 + 12 i } { 13 } }$
 Combine the fraction with the same denominator 
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 12 } \color{#FF6800}{ i } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \color{#FF6800}{ i } } { 13 }$
$\dfrac { - 5 \color{#FF6800}{ - } \color{#FF6800}{ 12 } \color{#FF6800}{ i } - 5 \color{#FF6800}{ + } \color{#FF6800}{ 12 } \color{#FF6800}{ i } } { 13 }$
 Eliminate opponent number 
$\dfrac { - 5 - 5 } { 13 }$
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } } { 13 }$
 Find the sum of the negative numbers 
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { 13 }$
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { 13 }$
 Move the minus sign to the front of the fraction 
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 10 } { 13 } }$
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