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Calculate the value
$\left( 3+4i \right) \left( 1-2i \right)$
$11 - 2 i$
Calculate the value
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ i } \right ) \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ i } \right )$
 Expand using $\left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ i } \right ) \color{#FF6800}{ + } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ i } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ i } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ i } \right )$
$3 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } + 3 \times \left ( - 2 i \right ) + \left ( 4 i \right ) \times 1 + \left ( 4 i \right ) \times \left ( - 2 i \right )$
 Multiplying any number by 1 does not change the value 
$\color{#FF6800}{ 3 } + 3 \times \left ( - 2 i \right ) + \left ( 4 i \right ) \times 1 + \left ( 4 i \right ) \times \left ( - 2 i \right )$
$3 + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ i } \right ) + \left ( 4 i \right ) \times 1 + \left ( 4 i \right ) \times \left ( - 2 i \right )$
 Get rid of unnecessary parentheses 
$3 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ i } + \left ( 4 i \right ) \times 1 + \left ( 4 i \right ) \times \left ( - 2 i \right )$
$3 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ i } + \left ( 4 i \right ) \times 1 + \left ( 4 i \right ) \times \left ( - 2 i \right )$
 Simplify the expression 
$3 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ i } + \left ( 4 i \right ) \times 1 + \left ( 4 i \right ) \times \left ( - 2 i \right )$
$3 - 6 i + \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ i } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 1 } + \left ( 4 i \right ) \times \left ( - 2 i \right )$
 Get rid of unnecessary parentheses 
$3 - 6 i + \color{#FF6800}{ 4 } \color{#FF6800}{ i } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } + \left ( 4 i \right ) \times \left ( - 2 i \right )$
$3 - 6 i + 4 i \color{#FF6800}{ \times } \color{#FF6800}{ 1 } + \left ( 4 i \right ) \times \left ( - 2 i \right )$
 Multiplying any number by 1 does not change the value 
$3 - 6 i + 4 i + \left ( 4 i \right ) \times \left ( - 2 i \right )$
$3 - 6 i + 4 i + \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ i } \right ) \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ i } \right )$
 Get rid of unnecessary parentheses 
$3 - 6 i + 4 i \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ i } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ i }$
$3 - 6 i + 4 i - 4 \color{#FF6800}{ i } \times 2 \color{#FF6800}{ i }$
 It is $i \times i = -1$
$3 - 6 i + 4 i - 4 \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \times 2$
$3 - 6 i + 4 i \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 2 }$
 Multiply the numbers 
$3 - 6 i + 4 i + \color{#FF6800}{ 8 }$
$\color{#FF6800}{ 3 } - 6 i + 4 i \color{#FF6800}{ + } \color{#FF6800}{ 8 }$
 Add $3$ and $8$
$\color{#FF6800}{ 11 } - 6 i + 4 i$
$11 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ i } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ i }$
 Calculate between similar terms 
$11 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ i }$
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